If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Projectile height given time

Figuring out how high a ball gets given how long it spends in the air. Created by Sal Khan.

## Want to join the conversation?

• so does this mean that if I project an elephant with a velocity of 24.5 m/s, it is going to reach the same height as a feather projected with the same velocity ? •   without air, yes.
but on earth air and shape of feather does not allow you to do that
also to project an elephant with that velocity would be such a pain.
• why is velocity final zero?? • I don't see how it's possible to derive the initial velocity on the up trip from knowing the velocity on the down trip. If I shoot a bullet in the air, it's going to travel faster on the up trip than on the down trip, isn't it? On the up trip it may go 24.5m/s^2 in 1s and on the down trip 9.8m/s^2 in 2.5s. Same overall displacement, but different velocities and accelerations. Unless I'm missing something... • The total distance that bullet travels vertical is equal in this case to the total distance travelled up and down. The inital velocity is going to be 'slowed' down to zero (m/s) because of gravity, and the effect will be equally the same returning. Therefore the acceleration/deaccelertion is equl, the distance is equal and so will the time. This will ultimately show that the velocity at the exact same elevation (height) will be the same.

If, the bullet hits and object higher than it was orginally fired, it will be travelling that much slower, and vice versa if the bullet travels below (say of a cliff) it will continue accelerating until impact.
• Could anyone please confirm the displacement of 30.6 meters is only for half the time. i.e. distance reached at halfway point. or is it the total distance? • So what exactly is air resistance, and why does everyone treat it as "negligible"? • There are two main effects that are part of air resistance.

One is the need for the object moving through the air to move the air out of the way as it move through it.

The second effect is drag which is caused as the air flows around an object there is usually a low pressure region created behind the object that acts to pull back on the object. The size of this effect depends on the overall shape of the object, there is less drag on a teardrop shaped object than a box.

Air resistance is treated as negligible in many problems because air has a low density and at speeds that are a small fraction of the speed of sound air resistance is a small effect.
• At is the initial velocity zero or the final velocity? Earlier in the video he said that the initial velocity is zero. • Even I was stuck at this but later got it:)
Sal said that the initial velocity is zero because the ball wasn't thrown yet and it was at rest.
Later he said that the final velocity is zero. Huh? Because when the ball was thrown up and it reached its final position, it again had to come down . Its new initial velocity was zero again because it had to come all the way down again and that was the `final velocity`.
Hope that helps:)
• When you are calculating displacement at the end... where do you get the equation to solve for it. I used the equation v(f)^2 = v(Initial)^2 + 2a(change in x)... However I get 3.125 meters instead... which should get the same value for the change in x as you but I didn't. What would I have to do differently to get the displacement of the object? • Well I did the calculations and for both V(F)^2 = V(0)^2 + 2ad and d = V(F) + V(0)/2 * t

Here's what I got:
d = V(F) + V(0)/2 * t
d = (-24.5 + 0)/2 * 2.5
d = -12.25 * 2.5
d = -30.625

-24.5^2 = 0^2 + 2(-9.8)d
600.25 = (-19.6)d
d = 600.25/-19.6
d = -30.625

The ball's initial velocity is the one measured at its highest point and its final velocity is the one right before it hit the ground, going downwards. In this case, the up is positive so having a negative displacement would mean it went down from its initial position.
• is the velocity calculated by Average on because both the rise and fall of the object is taken into question? • in the last video sal said that displacement is equal to initial velocity times time + 1/2 acceleration times time squared, but in this video an else formula was used by him, why?  