Catching Football (Projectile Motion)

[Toranc3]

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!

 

[rude man]

It is not made clear whether the initial velocity of the ball was in the qb's reference frame or that of the stadium ...

 

[Toranc3]

It is not made clear whether the initial velocity of the ball was in the qb's reference frame or that of the stadium ...

So what do we do?

 

[rude man]

So what do we do?

Ask the teacher what he meant. If it's a textbook question you can assume either case or work it both ways. Or ask your teacher what to assume.

EDIT:
I see you have already gotten the right equations. You've assumed the ball's initial v_x = 20cos(45) + 1.5 and I think this is the best assumption.

Your work is excellent! I got all the same equations and numerical answers I checked (I did not check all your math, just some of it).

 

[Toranc3]

Ask the teacher what he meant. If it's a textbook question you can assume either case or work it both ways. Or ask your teacher what to assume.

EDIT:
I see you have already gotten the right equations. You've assumed the ball's initial v_x = 20cos(45) + 1.5 and I think this is the best assumption.

Your work is excellent! I got all the same equations and numerical answers I checked (I did not check all your math, just some of it).

Ok I will. I had a quick question though, if the ball's velocity was with respect to the Earth would you just ignore the quarterback moving at 7m/s?

 

[rude man]

Ok I will. I had a quick question though, if the ball's velocity was with respect to the Earth would you just ignore the quarterback moving at 7m/s?

Yes, which is why the fact that they gave you his speed suggested that they meant that speed to be added to his x throwing velocity.

BTW I think his speed was 1.5 m/s. The fullback (or whoever) was running at 7.

Good work!

 

[Toranc3]

Yes, which is why the fact that they gave you his speed suggested that they meant that speed to be added to his x throwing velocity.

BTW I think his speed was 1.5 m/s. The fullback (or whoever) was running at 7.

Good work!

Thank you!