Help me with a Physics Type Question

[Tizz]

Any physics majors here? Maybe I'll get lucky but I'm having a debate with a friend over this concerning throwing a football.

I have two friends. We went out to throw catch some passes. They are both QBs. On like a 20 yard out route, Guy A hums that ball in there and I can hardly catch it, the velocity is so aggressive it hurts my hands. Guy B its not like that, its a softer throw with a bit of wobble and I have no trouble catching it. I told Guy B that Guy A has a much stronger arm than him and he disagreed, so he said lets have a contest to see who can throw the ball the FARTHEST. They both threw the ball 62 yards in the air. We measured it.

Guy B thinks he proved his point that his arm is equally as strong as Guy A, but I said then Guy A has much more velocity, and he said that isn't possible because in order to throw the same distance that means they have the same velocity. What do you guys think? Is there something in this equation we are missing?

[liftsiron]

I would expect that the harder thrown ball covers the 62 yards faster than the softer thrown ball. Although they both throw the same distance one throws with greater velocity.

[Bouncer]

to measure how truly strong there arm is, its a matter of distance and time.

so if they both can throw the ball 62 yards you need to time how fast it takes the ball once it leaves the hand to travel that 62 yards.

the person that can throw the ball the 62 yards in the shortest amount of time is the person with the stronger arm..


think of a drag race between 2 cars. they both can travel a mile but the faster and more powerful car will travel that mile much faster.

[Bouncer]

also have to take into account the angle at which the ball was thrown.

the ball that hit your hand harder obviously had more distance to travel.

if both balls are thrown at the exact same angle and travel the same exact path the ball traveling at the higher velocity will travel a further distance.

[Tizz]

so if they both can throw the ball 62 yards you need to time how fast it takes the ball once it leaves the hand to travel that 62 yards.

the person that can throw the ball the 62 yards in the shortest amount of time is the person with the stronger arm..

but if one truely does have more velocity than the other, then why is their maximum distance the same?

[decadecadeca]

but if one truely does have more velocity than the other, then why is their maximum distance the same?

Angle and arc.

[Bouncer]

Bingo ^

if they are thrown at the exact same angle and arc the ball with higher speed will travel farther.

[mofo]

if you throw two identical balls in the air at the same angle from the ground but with different forces, the ball with the stronger force (A) behind it will have a greater momentum and thus will not only accelerate to a higher speed but it will push the air particles out of it's path with a stronger force as well, clearing a greater distance. the ball with the lesser force behind it (B) will have less force to push air particles out of the way and will result in a shorter distance.

as for the two balls landing at the same distance but have difference forces behind them.

if you throw A at a higher angle, it has to deal with a greater force of gravity acting on it pulling it down harder decreasing the distance traveled. that is what makes it possible to have two different forces acting on the same ball but having the same result.

[Tizz]

Bingo ^

if they are thrown at the exact same angle and arc the ball with higher speed will travel farther.

Is there a maximum that such an object will go regardless of the force behind it? Do you ever reach a point to where no matter how much force is behind the object, it can only go so far?

[Bouncer]

Is there a maximum that such an object will go regardless of the force behind it? Do you ever reach a point to where no matter how much force is behind the object, it can only go so far?

if you were to drop a ball out of an airplane it would reach a speed where it can no longer go any faster. that is called terminal velocity. the point at which the air pushing back against the ball keeps it from moving any further.

BUT, if the ball were shot out of a canon or something like that the ball would be able to go past its terminal velocity. it would reach a point however that the force needed to launch the ball would be so great that it would destroy the ball itself.

[Scrumhalf]

For the original question, you get maximum distance by throwing at a 45 degree angle. If both throws are at a 45 degree angle, the person throwing with the higher velocity will throw the ball further.

It is easy to figure this out by considering the horizontal and vertical movements of the ball as independent of each other (these are orthogonal directions and hence it is legitimate to do so).

If the ball is thrown at 45 degrees, the vertical and horizontal velocities are both equal to sqrt (2) x the original velocity, that is 0.707 x the original velocity.

The total time the ball is in the air is the amount of time it takes the ball to go to its maximum height and then fall back down again to the throwing height (which we'll assume is also the height at which it is caught) - this is simply (2 x the vertical velocity) divided by the acceleration due to gravity which is 32 ft/s^2.

Once you know how long the ball is in the air, the distance it travels horizontally is simply equal to the horizontal velocity multiplied by the time it is in the air.

This ignores air resistance, etc. but at the speeds we are talking about, it is not a serious concern. The key is launching the ball at 45 degrees.

[Turbo3000]

if you were to drop a ball out of an airplane it would reach a speed where it can no longer go any faster. that is called terminal velocity. the point at which the air pushing back against the ball keeps it from moving any further.

BUT, if the ball were shot out of a canon or something like that the ball would be able to go past its terminal velocity. it would reach a point however that the force needed to launch the ball would be so great that it would destroy the ball itself.

What did you do with our leader Bouncer? How much is the ransom? :thumup:

[Scrumhalf]

For the second question, the maximum velocity objects can achieve in the atmosphere is usually limited by air resistance in all practical circumstances. It is possible to go faster by pushing it harder and harder but the amount of energy one has to expend grows exponentially with speed due to air resistance and it soon becomes impractical.

In space, there is no such problem. In fact, one idea for spacecraft propulsion uses the tiny momentum imparted by photons of light to literally use light for propulsion. The idea is called a solar sail - it involves a huge sail (could be kilometers across) that uses the light from the sun to push it along. The acceleration is extremely small, but since velocity is acceleration x time, given enough time, enormous speeds can be built up in the absence of air resistance.

[mofo]

who here has actually majored in physics? the original question is for a "physics major" but i'm pretty sure stuff like this is common knowledge. :P

[Scrumhalf]

Majored in Electrical Engineering, so learned plenty of physics. Didn't do too much particle physics, relativity, etc. which are more in a core physics curriculum, but did plenty of electromagnetics, dynamics, thermodynamics/statistical physics, etc.