   Chapter 3, Problem 43AP

Chapter
Section
Textbook Problem

A home run is hit in such a way that the baseball just clears a wall 21 m high, located 130 m from home plate. The ball is hit at an angle of 35° to the horizontal, and air resistance is negligible. Find (a) the initial speed of the ball, (b) the time it takes the ball to reach the wall, and (c) the velocity components and the speed of the ball when it reaches the wall. (Assume the ball is hit at a height of 1.0 m above the ground.)

(a)

To determine
The initial speed of the ball.

Explanation

At time t , the ball must be

Δy=21m1.0m=20.0m

Above its launch position.

So, the equation Δy=v0yt+12ayt2 becomes

Δy=v0sinθ(Δxv0cosθ)+12ay(Δxv0cosθ)2

Here,

v0 is the initial velocity

θ is the angle of projection

ay is the vertical acceleration

Δx is the horizontal displacement

Substitute 130m for Δx , 9.80m/s2 for ay , 20m for Δy and 35.0° for θ .

20m=v0sin35

(b)

To determine
The time it takes the ball to reach the wall.

(c)

To determine
The velocity components and the speed of the ball as it reaches the wall.

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