A quarterback claims that he can throw the football ahorizontal distance of 183 m (200 yd). Furthermore, he claims thathe can do this by launching the

Tahmid Knox

Tahmid Knox

Answered question

2021-02-16

A quarterback claims that he can throw the football ahorizontal distance of 183 m (200 yd). Furthermore, he claims thathe can do this by launching the ball at the relatively low angle of 30.0 degree above the horizontal. To evaluate this claim, determinethe speed with which this quarterback must throw the ball. Assumethat the ball is launched and caught at the same vertical level andthat air resistance can be ignored. For comparison, a baseballpitcher who can accurately throw a fastball at 45 m/s (100 mph)would be considered exceptional.

Answer & Explanation

faldduE

faldduE

Skilled2021-02-18Added 109 answers

For horizontal range of a projectile R=V02sin20g Hence V0=Rgsin20=1839.8sin60=45.5ms
Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-11Added 2605 answers

Let the velocity of throwing be y,

Consider the vertical motion of football,

We have equation of motion, v = u + at

At maximum height final velocity, v = 0

Initial velocity, u=ysin34.2=0.562y

Acceleration, a=9.81 m/s2

Substituting,

0=0.562y9.81t

t=0.562y9.81

Total time of flight = 2 x Time to reach maximum height

Total time of flight =2×0.562y9.81=0.115y

Consider the horizontal motion of football,

We have equation of motion , s=ut+0.5at2

Initial velocity , u=ycos34.2=0.827y

Acceleration, a=0m/s2

Total time of flight , t=0.115y

Substituting

s=0.827y×0.115y+0.5×0×(0.115y)2=0.095y2

This is the maximum horizontal distance he can throw,

Given that

0.095y2=161

y=41.14 m/s

The speed with which this quarterback must throw the ball = 41.14 m/s

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?