How can I find out how far the ball goes in this video? And does the hill have any effect on the distance?

Question

My boyfriend's video was posted on YouTube about 8 months ago and ever since, people have been commenting that his best friend can't throw the ball 100 yards because there is a hill involved.

They have me thinking now, and I still think they are wrong, because it's flying down the hill, not rolling. Also, I was wondering how far the ball really DID go.
This is the video: http://youtube.com/watch?v=nt4wgtuXe7k

I know this will take some (maybe) simple physics to figure out, but alas.... I never took physics. I'd still like to see the full explanation if you can find one! Thanks!

Answer 1

Depends how big the hill is, how hard he threw it, and how you measure the distance.

The amount of time the ball stayed airborne can be found by measuring how fast the ball was traveling when it left his hand (v) and the angle he threw it at (Theta or Q since that's as close to looking like theta as I can get).

The ball has an upward vertical velocity (v * sin Q) and gravity has a downward acceleration. This equation can be used to find the time (t) that the ball is in the air.

s_f = s_i + v*sin(Q)*t -1/2*g*t^2
where s_i is initial position (height of hill)
s_f is final position (bottom of hill, or zero)
v is velocity of ball
Q is angle of ball
g is 9.8 m/sec^2 or 32 ft/sec^2; acceleration due to gravity

You can rearrange this and solve for time using the quadratic equation.

Once you have the time the ball is airborne, you look at the horizontal velocity, using this equation (which is actually very similar to the previous one)
s_f=s_i + v*cos(Q)*t

The only difference is there is no horizontal acceleration (technically, you have air resistance, but it's very small) and you use the cosine of Q instead of the sine.
s_i is your starting position, or zero.
s_f is your final HORIZONTAL displacement.

To find how far the ball travelled along the hill, you have to plug the height of the hill and the HORIZONTAL displacement into the Pythagorean theroem.

d = sqrt( y^2 + x^2)
where d is the distance measured down the hill
y = height of hill
x = HORIZONTAL displacement

I can't watch you tube from this computer, but throwing a ball a 100 yards is easy if the hill's steep enough. For example, if you throw the ball straight down from the top of a 1000 foot cliff, the ball would obviously travel 333 yards, even though it had a horizontal displacement of 0. Ski jumpers measure their distance along the surface of the hill they're jumping on, not their horizontal displacement, which is why they achieve such huge numbers for their jumps.

Answer 2

The ball definitely went farther than it would have done because it was thrown downhill, and if it had been thrown on a flat surface it would have hit the ground sooner.

When you throw a ball like this, you can think of two components of the force:
1. the bit that you throw it upwards, fighting gravity
2. the bit that you throw it sideways, fighting nothing but air resistance

Gravity will pull the ball downwards. If you throw it up, gravity will slow its rise, and then reverse its movement so that it falls. Whilst it's doing this, it'll still be traveling sideways, depending on how hard you threw it.

Because he threw the ball to an area that was much lower than the one he was on, this gives the ball a lot more time before it eventually hits the ground. During that time, the ball continues to travel sideways. Thus, throwing downwards means you can throw a long "surface" distance.

Think about the extreme: there's a big hole into the middle of the earth. Throw in the ball. It could go for *miles* before hitting the ground. That's not because you're strong, it's just because the ground keeps "dropping away".

Answer 3

i form of agree, yet you obtain to undergo in innovations the audiences those action pictures are concentrated on. ie: adult males between sixteen and 24. i dont think of any of those action picture makers got down to create an artistically credible action picture, yet somewhat desire to make the main of the fulfillment of the recreation, and supply gaming followers some seen thrills. the only one i enjoyed became Silent Hill, i assumed this became performed incredibly nicely and created an identical ecosystem from the recreation.

Answer 4

looks to be about 60 yards