Question

A ball is thrown on a projectile path with an initial vertical velocity of 30 m/s. If the ball lands 90 m away, find the initial horizontal velocity.

Answer 1

to find the horizontal velocity you need to find how long the ball was in the air, because you are going to assume that the horizontal velocity is constant the whole time. So once you know how long the ball was in the air you can do: distance/time to get the horizontal velocity

1) use the y velocity to find the time it is in the air:

use equation Vfinal = Vinitial + acceleration*time --- so Vinitial is 30m/s and acceleration is -9.8m/s^2

we will use 0 for Vfinal, because when it reaches its peak the velocity is equal to 0

0 = 30m/s + (-9.8m/s^2) * time

solve for time: t = -30/(-9.8) which is about 3.06 seconds

this is the time to get to the peak, which is half the time it is in the air, so multiply 3.06 seconds by two to get the total time in the air which gives 6.12 seconds

2) use this time to find the horizontal velocity

90m/6.12s = horizontal velocity

so the horizontal velocity is approximately 14.7 m/s