   Chapter 5, Problem 29P

Chapter
Section
Textbook Problem

A 50.0-kg projectile is fired at an angle of 30.0° above the horizontal with an initial speed of 1.20 × 102 m/s from the top of a cliff 142 m above level ground, where the ground is taken to be y = 0. (a) What is the initial total mechanical energy of the projectile? (b) Suppose the projectile is traveling 85.0 m/s at its maximum height of y = 427 m. How much work has been done on the projectile by air friction? (c) What is the speed of the projectile immediately before it hits the ground if air friction does one and a half times as much work on the projectile when it is going down as it did when it was going up?

(a)

To determine
The initial total mechanical energy of the projectile.

Explanation

Given Info:

The mass of the projectile is 50.0kg .

The angle of the projectile with horizontal is 30.0° .

Initial speed of the projectile is 1.20×102m/s .

The height of the cliff is 142m .

Formula to calculate the initial total mechanical energy is,

(Etot)i=KEi+PEi=12mvi2+mghi

• m is mass of the projectile
• vi is the initial speed of the projectile
• g is acceleration due to gravity
• hi is the height of the cliff

Substitute 50.0kg for m, 1.20×102m/s for vi , 9

(b)

To determine
The total work done by air friction.

(c)

To determine
The speed of the projectile immediately before it hits the ground.

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