I need someone that knows physics. I have a test in 10 hrs and Im not good at it. Can anyone help me?

Answer:

A= The type of plant

B= How tall the plant is

Explanation:

Answer:

The youngest person

Explanation:

Hearing worsens with age

Please mark brainliest

Answer:

A

Explanation:

The person closest to the origin of the sound will most likely hear the loudest sound. ^^

Answer:

Explanation:

purchase price = 400 tepizes / m²

1 tepiz = .625 dollar

purchase price in terms of dollar = 400 x .625 dollar / m²

= 250 dollar / m²

.9144 m = 1 yard

1 m = 1.0936 yard

1m² = 1.196 yard²

price in terms of dollar / yards²

= 250 / 1.196 dollar / yard²

= 209 dollar / yard²

Price of cloth in New York = 120 dollar / yard²

loss = 209 - 120 = 89 dollar / yard²

500 m² = 500 x 1.196 yard²

= 598 yard²

net loss in purchasing 500 m² cloth

= 598 x 89

= 53222 dollar .

Answer:

2025m

Explanation:

Since all materials of the sphere is made to a cylindrical wire, it implies the volume of the sphere material is same as that of the cylinder. This is expressed mathematically thus.

Volume of Sphere= volume of cylinder

4/3 ×π×R^3= π× r2× L

4/3 ×R^3= r^2×L

Hence

L = 3/4 × R^3/ r^2

But R = 6.0/2 = 3.0cm{ Diameter is twice raduis}

r= 0.2/2 = 0.1mm=>0.01cm{ Diameter is twice raduis and unit converted by dividing by 10 since 10mm = 1cm}

Substituting R and r into the expression for L, we have :

L = 3/4 × 3^3/ 0.01^2= 0.75 ×27/0.0001 = 202500cm

202500/100= 2025m{ we divide by 100 because 100cm=1m}

Energy = (power) x (time)

-- For the toaster:

Power = 1.4 kW  =  1,400 watts

Time = 5.4 minutes = 324 seconds

Energy = (1,400 W) x (324 s)  =  453,600 Joules

-- For the CFL bulb:

Power = 11 watts

Time = 10.5 hours = 37,800 seconds

Energy = (11 W) x (37,800 s)  =  415,800 Joules

-- The toaster uses energy at 127 times the rate of the CFL bulb.

-- The CFL bulb uses energy at 0.0079 times the rate of the toaster.

-- The toaster is used for 0.0086 times as long as the CFL bulb.

-- The CFL bulb is used for 116.7 times as long as the toaster.    

-- The toaster uses 9.1% more energy than the CFL bulb.

-- The CFL bulb uses 8.3% less energy than the toaster.  

Answer:

a) v₀ₓ = v₀ cos θ , b) v_{oy} = v₀ sin θ , c) y = v_{oy}² / 2g,  y = 24.25 m

e) R = 138.46 m

Explanation:

This is a projectile launch exercise

a) let's use trigonometry to find the components of the initial velocity

  cos θ = v₀ₓ / v₀

  v₀ₓ = v₀ cos θ

v₀ₓ = 38 cos 35

v₀ₓ = 31.13 m / s

b) sin θ = [tex]v_{oy}[/tex] / v₀

    v_{oy} = v₀ sin θ

    v_{oy} = 38 sint 35

    v_{oy} = 21 80 m / s

c, d) to find the maximum height, the vertical speed is zero

     v_{y}² = v_{oy}² - 2 g y

     0 = [tex]v_{oy}[/tex]² - 2 gy

     y = v_{oy}² / 2g

let's calculate

     y = 21.80 2 / (2 9.8)

     y = 24.25 m

e) They ask to find the horizontal distance

    for this we can use the expression of reaches

       R = v₀² sin 2θ / g

let's calculate

      R = 38² sin (2 35) / 9.8

       R = 138.46 m

Answer:

11,700Newton

Explanation:

According to Newton's second law, Force = mass × acceleration

Given mass = 65kg.

Acceleration if the car can be gotten using one of the equation of motion as shown.

v² = u²+2as

v is the final velocity = 18m/s

u is the initial velocity = 0m/s

a is the acceleration

s is the distance travelled = 0.9m

On substitution;

18² = 0²+2a(0.9)

18² = 1.8a

a = 324/1.8

a = 180m/²

Net force acting on the body = 65×180

Net force acting on the body = 11,700Newton

Answer:

rt

Explanation:

Answer:D

Explanation:

Given

Same force is applied to each ball such that all have different masses

and Force is given by the product of mass and acceleration

[tex]F=m\times a[/tex]

[tex]a=\frac{F}{m}[/tex]

So acceleration of ball A

[tex]a_A=\frac{F}{0.5}=2F[/tex]

acceleration of ball B

[tex]a_B=\frac{F}{0.75}=\frac{4F}{3}=1.33F[/tex]

acceleration of ball C

[tex]a_C=\frac{F}{1}=F[/tex]

acceleration of ball D

[tex]a_D=\frac{F}{7.3}=\frac{F}{7.3}[/tex]

It is clear that acceleration of ball D is least.

Answer:

C

Explanation:

Because everything on Earth falls at the same speed, the masses of the balls do not matter. Since the acceleration due to gravity is constant, their speeds will both be increasing at the same rate, and therefore the difference in speeds would remain constant until they hit the ground. Hope this helps!

Answer:

Explanation:

capacitance of air capacitor

C = ε₀ A /  d

ε₀ is permittivity of medium , A is plate area , d is distance between plate .

C = 8.85 x 10⁻¹² x 25 x 10⁻⁴ / 1.3 x 10⁻²

= 170.19 x 10⁻¹⁴ F .

charge on the capacitor when it is charged to  potential of 255 V

= CV , C is capacitance and V is potential

= 170.19 x 10⁻¹⁴  x 255

= 4.34 x 10⁻¹⁰ C .

After it is disconnected from the source , and it is immersed in water , charge on it remains the same .

So its charge when immersed in water will be constant at 4.34 x 10⁻¹⁰ C.

b )

When it is immersed in water its capacity increases  k times where k is dielectric constant of water which is 80 .

capacitance of capacitor in water = 80 x 170.19 x 10⁻¹⁴  F

= 13615.2  x 10⁻¹⁴ F .

= 1.36 x 10⁻¹⁰ F

potential difference = charge / capacitance

= 4.34 x 10⁻¹⁰ / 1.36 x 10⁻¹⁰

= 3.2 V

c )

Energy of capacitor = 1/2 C V²

Initial energy = 1/2 x 170.19 x 255² x 10⁻¹⁴

=  55.33 x 10⁻⁹ J

Final energy = 1/2 x 1.36 x 10⁻¹⁰ x 3.2²

= .7  x 10⁻⁹ J .

decrease of energy = 54.63 x 10⁻⁹ J .

Answer:

Air resistance

Answer B is correct

Explanation:

The friction that occurs when air pushes against a moving object causing it to negatively accelerate is called as air resistance.

hope this helps

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Answer:

The minimum frequency of the coil is 7.1 Hz

Explanation:

Given;

number of turns, N = 200 turns

cross sectional area, A = 300 cm² = 300 x 10⁻⁴ m²

magnitude of magnetic field strength, B = 30 x 10⁻³ T

maximum value of the induced emf, E = 8 V

Maximum induced emf is given as;

E = NBAω

where

ω is angular velocity (ω = 2πf)

E = NBA2πf

where;

f is the minimum frequency, measured in hertz (Hz)

f = E / (NBA2π)

f = 8 / (200 x 30 x 10⁻³  x 300 x 10⁻⁴ x 2 x 3.142)

f = 7.073 Hz

f = 7.1 Hz

Therefore, the minimum frequency of the coil is 7.1 Hz

The minimum frequency of the coil in the case when it should be rotated in a uniform 30-mT magnetic field is 7.1 Hz.

Since

number of turns, N = 200 turns

cross-sectional area, A = 300 cm² = 300 x 10⁻⁴ m²

the magnitude of magnetic field strength, B = 30 x 10⁻³ T

the maximum value of the induced emf, E = 8 V

Now

Maximum induced emf should be

E = NBAω

here,

ω is angular velocity (ω = 2πf)

Now

E = NBA2πf

here,

f is the minimum frequency

So,

f = E / (NBA2π)

f = 8 / (200 x 30 x 10⁻³  x 300 x 10⁻⁴ x 2 x 3.142)

f = 7.073 Hz

f = 7.1 Hz

Therefore, the minimum frequency of the coil is 7.1 Hz.

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Answer:

The centripetal acceleration of the traveler is [tex]40.98\ m/s^2[/tex]

Explanation:

It is given that, A carousel has a diameter of 6.0-m and completes one rotation every 1.7 s.

We need to find the centripetal acceleration of the traveler. It is given by the formula as follows :

[tex]a=\dfrac{v^2}{r}[/tex]

r is radius of carousel

[tex]v=\dfrac{2\pi r}{T}[/tex]

So,

[tex]a=\dfrac{4\pi ^2r}{T^2}[/tex]

Plugging all the values we get :

[tex]a=\dfrac{4\pi ^2\times 3}{(1.7)^2}\\\\a=40.98\ m/s^2[/tex]

So, the centripetal acceleration of the traveler is [tex]40.98\ m/s^2[/tex].

Answer:

A₁/A₂ = 0.44

Explanation:

The emissive power of the bulb is given by the formula:

P = σεAT⁴

where,

P = Emissive Power

σ = Stefan-Boltzman constant

ε = Emissivity

A = Surface Area

T = Absolute Temperature of Surface

FOR BULB 1:

Since, emissivity and emissive power are constant.

Therefore,

P = σεA₁T₁⁴   ----------- equation 1

where,

A₁ = Surface Area of Bulb 1

T₁ = Temperature of Bulb 1 = 3000 k

FOR BULB 2:

Since, emissivity and emissive power are constant.

Therefore,

P = σεA₂T₂⁴   ----------- equation 2

where,

A₂ = Surface Area of Bulb 2

T₂ = Temperature of Bulb 1 = 2000 k

Dividing equation 1 by equation 2, we get:

P/P = σεA₁T₁⁴/σεA₂T₂⁴

1 = A₁(3000)²/A₂(2000)²

A₁/A₂ = (2000)²/(3000)²

A₁/A₂ = 0.44

Answer:

a) t = 27.00 h

b) B = 6.84 MeV/nucleon

Explanation:

a) The time can be calculated using the following equation:

[tex] R = R_{0}e^{-\lambda*t} [/tex]

Where:

R: is the radiation measured at time t

R₀: is the initial radiation

λ: is the decay constant

t: is the time

The decay constant can be calculated as follows:

[tex] t_{1/2} = \frac{ln(2)}{\lambda} [/tex]

Where:

t(1/2): is the half life = 4.5 h

[tex] \lambda = \frac{ln(2)}{t_{1/2}} = \frac{ln(2)}{4.5 h} = 0.154 h^{-1} [/tex]

We have that the radiation measured is 64 times the maximum permissible level, thus R₀ = 64R:  

[tex] \frac{R}{64R} = e^{-\lambda*t} [/tex]                      

[tex] t = -\frac{ln(1/64)}{\lambda} = -\frac{ln(1/64)}{0.154 h^{-1}} = 27.00 h [/tex]            

b) The binding energy (B) can be calculated using the following equation:

[tex]B = \frac{(Z*m_{p} + N*m_{n} - M_{A})}{A}*931.49 MeV/u[/tex]

Where:

Z: is the number of protons = 2 (for [tex]^{4}_{2}He[/tex])

[tex]m_{p}[/tex]: is the proton mass = 1.00730 u

N: is the number of neutrons = 2 (for [tex]^{4}_{2}He[/tex])

[tex]m_{n}[/tex]: is the neutron mass = 1.00869 u  

[tex]M_{A}[/tex]: is the mass of the He atom = 4.002602 u

A =  N + Z = 2 + 2 = 4    

The binding energy of [tex]^{4}_{2}He[/tex] is:

[tex]B = \frac{(2*1.00730 + 2*1.00869 - 4.002602)}{4}*931.49 MeV/u = 7.35\cdot 10^{-3} u*931.49 MeV/u = 6.84 MeV/nucleon[/tex]

Hence, the binding energy per nucleon is 6.84 MeV.

I hope it helps you!

Answer:

a. the initial velocity of the cat is 5.95 m/s at 60.2° from the horizontal

b. 0.847 m

Explanation:

a. Using v² = u² + 2as, we find the initial vertical velocity of the cat. Now at the peak height, v = final velocity = 0, u = initial velocity and a = -g = 9.8 m/s², s vertical distance travelled by the cat from its position on the cabinet = Δy = 3.130 m - 1.765 m = 1.365 m.

Substituting these variables into the equation, we have

0² = u² + 2(-9.8m/s²) × 1.365 m

-u² = -26.754 m²/s²

u = √26.754 m²/s²

u = 5.17 m/s

To find its initial horizontal velocity, u₁ we first find the time t it takes to reach the peak height from

v = u + at. where the variables mean the same as above.

substituting the values, we have

0 = 5.17 m/s +(-9.8m/s²)t

-5.17 m/s = -9.8m/s²t

t = -5.17 m/s ÷ (-9.8m/s²)

= 0.53 s

Now, the horizontal distance d = u₁t = 1.560 m

u₁ = d/t = 1.560 m/0.53 s = 2.96 m/s

So, the initial velocity of the cat is V = √(u² + u₁²)

= √((5.17 m/s)² + (2.96 m/s)²)

= √(26.729(m/s)² + 8.762(m/s)²)

= √(35.491 (m/s)²)

= 5.95 m/s

its direction θ = tan⁻¹(5.17 m/s ÷ 2.96 m/s) = 60.2°

So, the initial velocity of the cat is 5.95 m/s at 60.2° from the horizontal

(b)

First, we find the time t' it takes the cat to land on the bed from d' = u₁t'

where d' = horizontal distance of cabinet from bed = 3.582 m

u₁ = horizontal velocity = 2.96 m/s

t' = d'/u₁

= 3.582 m/2.96 m/s

= 1.21 s

The vertical between the bed and cabinet which is the vertical distance moved by the cat is gotten from Δy = ut' +1/2at'²

substituting u = initial vertical velocity = 5.17 m/s, t' = 1.21 s and a = -g = -9.8 m/s² into Δy, we have  

Δy = ut' +1/2at'² = 5.17 m/s × 1.21 s +1/2(- 9.8 m/s²) × (1.21 s)² = 6.256 - 7.174 = -0.918 m

Δy = y₂ - y₁

Since our initial position is the position of the cabinet above the ground = y₁ = 1.765 m

y₂ = position of bed above ground.

Δy = y₂ - y₁ = -0.918 m

y₂ - 1.765 m = -0.918 m

y₂ = 1.765 m - 0.918 m

= 0.847 m

Answer:

D. Presynaptic terminal button

explanation:

Terminal Buttons are small knobs at the end of an axon that release chemicals called neurotransmitters. The terminal buttons form the Presynaptic Neuron

hope this helped!

Explanation:

Momentum = mass × velocity

p = mv

p = (1000 kg) (14 m/s)

p = 14000 kg m/s

The momentum of the car as it moves down the highway at the given speed is 14000-kg.m/s

Given the data in the question

Momentum is the product of the mass of a particle and its velocity.

Momentum = Mass × Velocity

[tex]P = m \ * \ v[/tex]

We substitute our given values into the equation

[tex]P = 1000kg \ * \ 14m/s\\\\P = 14000kg.m/s[/tex]

Therefore, the momentum of the car as it moves down the highway at the given speed is 14000-kg.m/s

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Answer:

a bale

Explanation:

a bale is a group of turtles

Answer:

A bale or nest

Explanation:

Answer:

The maximum speed v that the car can go without flying off the track = 15.29 m/s

Explanation:

let us first lay out the information clearly:

mass of car (m) = 410 kg

radius of race track (r) = 83.4 m

coefficient of friction (μ) = 0.286

acceleration due to gravity (g) = 9.8 m/s²

maximum speed = v m/s

For a body in a constant circular motion, the centripetal for (F) acting on the body is given by:

F = mass × ω

where:

F = maximum centripetal force = mass × μ × g

ω = angular acceleration = [tex]\frac{(velocity)^2}{radius}[/tex]

∴ F = mass × ω

m × μ × g = m × [tex]\frac{v^{2} }{r}[/tex]

410 × 0.286 × 9.8 = 410 × [tex]\frac{v^{2} }{83.4}[/tex]

since 410 is on both sides, they will cancel out:

0.286 × 9.8 = [tex]\frac{v^{2} }{83.4}[/tex]

2.8028 = [tex]\frac{v^{2} }{83.4}[/tex]

now, we cross-multiply the equation

2.8028 × 83.4 = [tex]v^{2}[/tex]

[tex]v^{2}[/tex] = 233.754

∴ v = √(233.754)

v = 15.29 m/s

Therefore, the maximum speed v that the car can go without flying off the track = 15.29 m/s

Answer:

Plutonium–238

Explanation:

The stability of isotopes is largely dependent on their half-life.

Half life of an isotope is the time taken for the initial mass of the isotope to be halfed or we can say that the half-life of an isotope is the time taken for the mass of the isotope to become half the initial mass.

From the above definition, we discovered that if the time taken for the mass of the isotope to become half its initial mass is long, then the isotope must be very stable. On the other hand, if the time taken to become half its initial mass is short, then the isotope is unstable because.

We can thus say that, the longer the half-life the more stable the isotope and the shorter the half-life, the less stable the isotope will be.

Considering the table given in the question above and with the ideas we have obtained from the explanation above, we can see that Plutonium–238 has the longest half-life. Therefore Plutonium–238 will be more stable.

Complete question is:

A 1200 kg car reaches the top of a 100 m high hill at A with a speed vA. What is the value of vA that will allow the car to coast in neutral so as to just reach the top of the 150 m high hill at B with vB = 0 m/s. Neglect friction.

Answer:

(V_A) = 31.32 m/s

Explanation:

We are given;

car's mass, m = 1200 kg

h_A = 100 m

h_B = 150 m

v_B = 0 m/s

From law of conservation of energy,

the distance from point A to B is;

h = 150m - 100 m = 50 m

From Newton's equations of motion;

v² = u² + 2gh

Thus;

(V_B)² = (V_A)² + (-2gh)

(negative next to g because it's going against gravity)

Thus;

(V_B)² = (V_A)² - (2gh)

Plugging in the relevant values;

0² = (V_A)² - 2(9.81 × 50)

(V_A) = √981

(V_A) = 31.32 m/s

Answer:

a) a = 3.09 m/s²

b) aₓ = 2.60 m/s²

Explanation:

a) The magnitude of her acceleration can be calculated using the following equation:

[tex] V_{f}^{2} = V_{0}^{2} + 2ad [/tex]

Where:

[tex]V_{f}[/tex]: is the final speed = 8.89 m/s

[tex]V_{0}[/tex]: is the initial speed = 0 (since she starts from rest)

a: is the acceleration

d: is the distance = 12.8 m    

[tex] a = \frac{V_{f}^{2}}{2d} = \frac{(8.89 m/s)^{2}}{2*12.8 m} = 3.09 m/s^{2} [/tex]

Therefore, the magnitude of her acceleration is 3.09 m/s².              

b) The component of her acceleration that is parallel to the ground is given by:

[tex] a_{x} = a*cos(\theta) [/tex]

Where:

θ: is the angle respect to the ground = 32.6 °

[tex] a_{x} = 3.09 m/s^{2}*cos(32.6) = 2.60 m/s^{2} [/tex]

Hence, the component of her acceleration that is parallel to the ground is 2.60 m/s².

I hope it helps you!

A skateboarder, starting from rest, rolls down a 12.8-m ramp the magnitude of the skateboarder's acceleration is approximately 3.07 [tex]m/s^2[/tex], the component of her acceleration that is parallel to the ground is approximately 1.66 [tex]m/s^2[/tex].

(a) The following kinematic equation can be used to calculate the skateboarder's acceleration:

[tex]v^2 = u^2 + 2as[/tex]

[tex](8.89)^2 = (0)^2 + 2a(12.8)[/tex]

78.72 = 25.6a

a = 78.72 / 25.6

a = 3.07 [tex]m/s^2[/tex]

(b) Trigonometry can be used to calculate the part of her acceleration that is parallel to the ground. We are aware that the ramp's angle with the ground is 32.6°.

[tex]a_{parallel }= a * sin(\theta)[/tex]

Plugging in the values:

[tex]a_{parallel[/tex] = 3.07  [tex]m/s^2[/tex]* sin(32.6°)

[tex]a_{parallel[/tex]≈ 1.66  [tex]m/s^2[/tex]

Therefore, the component of her acceleration that is parallel to the ground is approximately 1.66  [tex]m/s^2[/tex].

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Answer:

2.95m

Explanation:

The farthest distance the object can move is the radius of the circle of which the Simple harmonic motion is assumed to be a part

But V = w× r; where V is velocity,

w is angular velocity and r is radius.

Also,

a= w2r; where a is linear acceleration

but a = v× r ; by comparing both equations

Hence r = a/v =8.6/2.45 =3.51m

But the horizontal distance of the motion is given by:

X = rcosx ; where x is the angle

X is the distance covered.

We know that the maximum value of cos x is 1 which is 0°

When the object moves in a fashion directly parallel to an horizontal distance, maximum distance would be reached and hence:

X = r=3.51m

Meaning the object needs to travel 3.51-0.56=2.95m further.

Note: the acceleration of the motion is constant whether it is swinging towards the left or right.

When the object is displaced 0.560 m to the right of its equilibrium position, it has a velocity of 2.45 m/s to the right and an acceleration of 8.60 m/s2 to the left and the amplitude of motion A = 0.732 m.

The distance between the central and extreme points for a moving particle is known as the amplitude of motion.

The given data to find the amplitude of motion,

Object displaced = 0.560 m

Velocity = 2.45 m/s

Acceleration = 8.60 m/s²

Starting with sine:

x(t) = Asin(ωt)

so that t = 0, x = 0

x(t) = 0.56 m = Asin(ωt)

v(t) = x(t)'= 2.45 m/s = Aωcos(ωt)

a(t) = v(t)'= -8.60 m/s² = -Aω²sin(ωt)

x(t) / a(t) = Asin(ωt) / -Aω²sin(ωt)

0.56m / -8.60 m/s² = -1 / ω²

ω² = 15.3571 rad^2/s^2

ω = 3.91881 rad/s  

x(t) / v(t) = Asin(ωt) / Aωcos(ωt)

0.560m / 2.45m/s = tan(3.91t) / 3.91rad/s

0.8937= tan(3.91t)

t = 0.176 s  

x(0.176) = Asin(3.59×0.176)

0.65 m= Asin(0.631)

A = 0.732 m is the amplitude of motion.

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Answer:

N = 243.596 N ≈ 243.6 N

Explanation:

mass of person = 69 kg ( M )

mass of aluminium ladder = 11 kg ( m )

length of ladder = 6.4 m ( l )

base of ladder = 2 m from the house (d )

center of mass of ladder = 2 m from the bottom of ladder

person on ladder standing = 3 m from bottom of ladder

Calculate the magnitudes of the forces at the top and bottom of the ladder

The net torque on the ladder = o ( since it is at equilibrium )

assuming: the weight of the person( mg) acting at a distance x along the ladder. the weight of the ladder ( mg) acting halfway along the ladder and the reaction N acting on top of the ladder

X = l/2

x = 6.4 / 2 = 3.2

find angle formed by the ladder

cos ∅ = d/l

    ∅ = [tex]cos^{-1][/tex] 2/6.4 = [tex]cos^{-1}[/tex]0.3125  ≈ 71.79⁰

remember the net torque around is = zero

to calculate the magnitude of forces on the ladder we apply the following formula

[tex]N = \frac{mg(dcosteta)+ Mgxcosteta}{lsinteta}[/tex]

m = 11 kg, M = 69 kg, l = 6.4 , x = 3,  teta( ∅ )= 71.79⁰, g = 9.8

back to equation  N = [tex]\frac{11*9.8(2*cos71.79)+ 69*9.8*3* cos71.79}{6.4sin71.79}[/tex]

N = (67.375 + 633.938) / 2.879

N = 243.596 N ≈ 243.6 N

Answer:

Distance = 16.9 m

Explanation:

We are given;

Power; P = 70 W

Intensity; I = 0.0195 W/m²

Now, for a spherical sound wave, the intensity in the radial direction is expressed as a function of distance r from the center of the sphere and is given by the expression;

I = Power/Unit area = P/(4πr²)

where;

P is the sound power

r is the distance.

Thus;

Making r the subject, we have;

r² = P/4πI

r = √(P/4πI)

r = √(70/(4π*0.0195))

r = √285.6627

r = 16.9 m

Answer:

16.9 m

Explanation:

Answer:

A. we will see that the notion [tex]\mathbf{|r ^ \to - r_2 ^\to| = 2.10006 \ m}[/tex] which denotes Stephen Curry  illustrates that Stephen Curry minigolf ball shot is closer

B.  Lebron James hits at an angle of 17.48° North -East.

The direction of Stephen is   = 20° due to East of North

Explanation:

Let [tex]r ^ {\to[/tex] represent the position vector of the hole;

Also; using  the origin as starting point. Let the east direction be along the positive x axis and the North direction  be + y axis

Thus:

[tex]r ^ {\to[/tex]  = [tex]8.2 \ sin 20^0 \hat i + 8.2 \ cos 20 \hat j[/tex]

[tex]r ^ {\to[/tex]  = [tex](2.8046 \hat i + 7.7055 \hat j ) m[/tex]

Let [tex]r_1 ^ \to[/tex] be the position vector for Lebron James's first shot

So;

[tex]r_1 ^ \to[/tex] = [tex](8.6 \ sin \ 35.2 )^0 \hat i + 8.6 \ cos \ ( 35.2)^0 \hat j[/tex]

[tex]r^ \to = (4.9573 \hat i + 7.02745 \hat j) m[/tex]

Let [tex]r_2 ^ \to[/tex] be the position vector for Stephen Curry's shot

[tex]r_2 ^ \to[/tex]  [tex]=6.1 \ sin 20^0 \hat i + 6.1 \ cos \ 20 \hat j[/tex]

[tex]r_2 ^ \to[/tex]  = [tex](2.0863 \hat i + 5.7321 \hat j )m[/tex]

However;

[tex]r ^ \to - r_1 ^\to = (-2.1527 \hat i + 0.67805 \hat j) m[/tex]

[tex]\mathbf{|r ^ \to - r_1 ^\to| =2.25696 \ m }[/tex]

Also;

[tex]r ^ \to - r_2 ^\to = (0.71013 \hat i - 1.9734 \hat j) m[/tex]

[tex]\mathbf{|r ^ \to - r_2 ^\to| = 2.10006 \ m}[/tex]

Thus; from above ; we will see that the notion [tex]\mathbf{|r ^ \to - r_2 ^\to| = 2.10006 \ m}[/tex] which denotes Stephen Curry  illustrates that Stephen Curry minigolf ball shot is closer

B .

For Lebron James ;

The angle can be determine using the trigonometric function:

[tex]tan \theta = ( \dfrac{0.67805}{-2.1527}) \\ \\ tan \theta = -0.131498 \\ \\ \theta = tan ^{-1} ( -0.31498) \\ \\ \mathbf{\theta = -17.48^0}[/tex]

Thus  Lebron James hits at an angle of 17.48° North -East.

For Stephen Curry;

[tex]tan \theta = ( \dfrac{-1.9734}{0.7183}) \\ \\ tan \theta = -2.74732 \\ \\ \theta = tan ^{-1} ( -2.74732) \\ \\ \mathbf{\theta = -70.0^0}[/tex]

The direction of Stephen is  = 90° - 70° = 20° due to East of North

Complete Question

A small car and an SUV are at a stoplight. The car has amass equal to half that of the SUV, and the SUV's engine can produce a maximum force equal to twice that of the car. When the light turns green, both drivers floor it at the same time. Which vehicle pulls ahead of the other vehicle after a few seconds?

a) It is a tie.

b) The SUV

c) The car

Answer:

The correct option is  a

Explanation:

From the question we are told that

     The mass of the car is [tex]m_c[/tex]

     The force of the car is  F

       The mass of the SUV is  [tex]m_s = 2 m_c[/tex]

       The force of the SUV is [tex]F_s = 2 F[/tex]

Generally force  of the car is mathematically represented as

        [tex]F= m_ca_c[/tex]

[tex]a_c[/tex] is acceleration of the car

Generally force  of the car is mathematically represented as

       [tex]F_s = m_s * a_s[/tex]

[tex]a_s[/tex] is acceleration of the SUV

=>   [tex]2 F = 2 m_c a_s[/tex]

       [tex]F = m_c a_s[/tex]

=>    [tex]m_c a_s = m_ca_c[/tex]

So  [tex]a_s = a_c[/tex]

  This means that the acceleration of both the car and the SUV are the same

Answer:

Explanation:

From Newton's second Law of Motion,

F = ma

Ff + F = ma

Where F is the applied force, Ff is the frictional force, a is the acceleration and m is the mass of the object or box.

Magnitude of the acceleration:

a = Ff+F/m

This must act in the direction of F or the box would slide or accelerate off the negative side of the board (taking the direction of F to be positive