Question

A car is initially at rest at the top of a hill with an incline of 25.0 degrees. The road down the hill is 40.0 m long and ends at the edge of a vertical cliff 100 m in height. 1. What is the acceleration of the car down the hill? 2. How long until the car reached the end of the road? 3. What is the velocity of the car at the end of the road? 4. How long doe it take for the car to fall the 100 m to the base of the cliff? 5. How far from the base of the cliff does the car strike the ground?

Answer 1

Given data θ=25°

length of incline , l = 40 m

1) Finding the acceleration

The acceleration of the car ,

a = g * sin(θ)

a = 9.81 * sin(25)

a= 4.15 m/s ²

2) Finding how long does car reached the end of rod

Assuming the time taken be t

We got acceleration, a=4.14 m/s ²

Initial velocity u=0

D=u t+1/2 at ²

Here we have to find t

We know t= sqrt 2 d/a

       t=sqrt *40/4.14

     t=4.39 sec

t=4.4 sec

3) Finding the velocity

Here the velocity of car ,

|v| = √(2 * a * l)

|v| =√ (2*4.15 * 40)

v= 18.2 m/s

4) How long does it take for the car to fall the 100 m to the base of the cliff

Assuming the time taken to fall 100 m be t ²

h = 100 m

= v * sin(θ) * t 2 + 0.5 * g * t ₂²

100 = 18.2 * sin(25) * t 2 + 0.5 * 9.81 * t ₂ ²

solving for t ₂

100=7.691*t 2+0.5*9.81*t ₂ ²

t 2 = 3.8 s

5) Finding the distance x

the distance from the base , x = v * cos (θ)* t ²

x = 18.2 * cos (25) * 3.8 m

x = 62.6 m