00:02
Alright, so for this problem, we're trying to find the max height that the ball goes.
00:10
So we have acceleration, velocity, and position, and these are all the initial measurements of those, and there's an inherent relationship between position, velocity, and acceleration, where acceleration's the derivative of velocity, and velocity is the derivative of acceleration.
00:30
So we know that r prime prime of 0 equals negative 32, and then that would make r prime of t equal negative 32, t plus 60 because r prime of 0 has to equal 60 and then r of t would then equal negative 16 t squared plus 60 t plus 6 because r 0 has to equal 6 so when all the t's are 0 it equals 6.
01:22
So now, when a ball reaches its max height, it's going to start here, be thrown up, and then come back down.
01:33
So what we know about this point is it's when the velocity changes from being positive to negative.
01:42
So at the max height, the velocity is going to be 0.
01:46
So to solve for the time this happens, we're going to plug 0 into the velocity.
01:51
Or r prime equation.
01:53
So r prime of 0 equals negative 32t plus 60...