- #1

Toranc3

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## Homework Statement

In a football game, a quarterback passed a ball to a receiver while running at 1.5 m/s

forward. The ball was released at a height of 2.5 meters with an angle of 45 degrees and

an initial velocity of 20 m/s. The receiver ran from behind to catch the ball at a height of

2 m.

a) Find the range or distance traveled by the ball.

b) Find the initial distance between the receiver and the quarterback, if the

receiver ran at constant velocity of 7 m/s to catch the ball. Assume he

started running at the same time as the ball was thrown.

c) Find the final velocity of the ball and its direction.

## Homework Equations

y=yo+voy*t + 1/2*a*t^(2)

x=xo+vox*t

Vb/e=Vb/q + Vq/e

Vb/e= velocity of ball relative to the earth

Vb/q= velocity of ball relative to quarterback

Vb/e= velocity of quarterback relative to earth

## The Attempt at a Solution

Vb/e-x= Vb/q-x + Vq/e-x

Vb/e-x= 20cos(45) + 1.5= 15.64m/s

Vb/e-y= Vb/q-y + Vq/e-y

Vb/e-y = 20sn(45) + 0= 14.14m/s

y=yo+voy*t + 1/2*a*t^(2)

2=2.5 + 14.14*t - 4.905*t^(2)

(quadratic formula)

t= 3.20

A) x= xo + vox*t

x= 15.64*(3.2015)= 50.07m

B) x= xo + vox*t

50.07=xo +7*(3.2015)

Xo = 27.6675m

C) Vy= Voy*t +a*t

Vy= 14.12 - 9.81(3.2015) = -17.28m/s

Vb/e= 23.29m/s

θ= -47.8 South of East

Is my work correct? May be a little long but thanks for checking!