   Chapter 3, Problem 15P

Chapter
Section
Textbook Problem

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 4.00 m/s2 for a distance of 50.0 m to the edge of the cliff, which is 30.0 m above the ocean. Find (a) the car’s position relative to the base of the cliff when the car lands in the ocean and (b) the length of time the car is in the air.

(a)

To determine
The car’s position relative to the base of the cliff when the car lands in the ocean.

Explanation

The speed of the car when it reaches the edge of the cliff is,

v=v02+2a(Δx)

Substitute 0m/s for v0 , 4.00m/s2 for a and 50.0m Δx .

v=(0m)2+2(4.00m/s2)(50.0m)=20.0m/s

Consider the projectile motion of the car, the vertical velocity of the car as it reaches the water is,

vy=v0y2+2ay(Δy)=(v0sinθ)+2ay(Δy)

Substitute 20.0m/s for v0 , 24.0° for θ , 9.80m/s2 for ay and 30.0m Δy .

vy=((20.0m/s)sin24.0°)2+2(9.80m/s2)(30

(b)

To determine
The length of time the car is in the air.

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