# Catching Football (Projectile Motion)

• Toranc3
In summary, the conversation discusses a scenario in which a quarterback throws a football to a receiver while both are in motion. Using given information and equations, the distance traveled by the ball is found to be 50.07m and the initial distance between the receiver and quarterback is calculated to be 27.6675m. The final velocity of the ball is found to be 23.29m/s at an angle of -47.8 degrees south of east. The conversation also raises a question about the initial velocity of the ball and the reference frame it is in, which prompts the suggestion of checking with the teacher for clarification. The expert summarizer praises the original poster's work as excellent and confirms that the correct equations were used.
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)
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!

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

rude man said:
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?

Toranc3 said:
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).

Last edited:
rude man said:
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?

Toranc3 said:
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!

rude man said:
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!

## What is the concept of "Catching Football (Projectile Motion)"?

The concept of "Catching Football (Projectile Motion)" refers to the physics involved in catching a football that is thrown or kicked through the air. It involves understanding the motion of the football as a projectile and applying principles of velocity, acceleration, and force to successfully catch the ball.

## How does the angle of the throw affect the motion of the football?

The angle of the throw directly affects the trajectory or path of the football. A higher angle will result in a higher arc, while a lower angle will result in a flatter trajectory. The angle also determines the range of the throw, with a higher angle resulting in a longer range and a lower angle resulting in a shorter range.

## What factors affect the distance a football can be thrown?

The distance a football can be thrown is affected by several factors, including the initial velocity, the angle of the throw, and air resistance. A higher initial velocity and a lower angle will result in a longer throw, while air resistance can decrease the distance by slowing down the football as it travels through the air.

## How does the weight of the football affect its trajectory?

The weight of the football does not significantly affect its trajectory, as long as it is within the standard weight range for footballs. However, a heavier football may be more difficult to throw and catch due to its increased inertia and force of impact.

## What are some real-life applications of understanding "Catching Football (Projectile Motion)"?

Understanding the physics of catching a football can have practical applications in sports such as football, rugby, and soccer. It can also be applied in other fields such as engineering and physics, where the principles of projectile motion are used to design and analyze the motion of objects.

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