   Chapter 3, Problem 45AP

Chapter
Section
Textbook Problem

A quarterback throws a football toward a receiver with an initial speed of 20. m/s at an angle of 30.° above the horizontal. At that instant the receiver is 20. m from the quarterback. In (a) what direction and (b) with what constant speed should the receiver run in order to catch the football at the level at which it was thrown?

(a)

To determine
The direction the receiver should run to catch the football at the level at which it was thrown.

Explanation

The equation for vertical displacement is,

Δy=v0yt+12ayt2=(v0sinθ)t+12ayt2

Here,

θ is the angle

v0 is the initial velocity

v0y is the vertical component of the initial velocity

ay is the vertical acceleration

t is the time taken

Substitute 20m/s for v0 , 0m for Δy , 30° for θ and 9.80m/s2 for ay .

0=[(20m/s)sin30°]t12(9

(b)

To determine
The constant speed the receiver should run to catch the football at the level at which it was thrown.

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