00:01
For this problem, we are told that a ballast is dropped from a stationary hot air balloon that is hovering at an altitude of 400 feet.
00:07
The velocity of the ballast after t seconds is negative 32t plus 4 feet per second.
00:12
In part a, we are asked to find the height h of the ballast from the ground at time t.
00:17
So what we can do here is find the antiderivative of that h prime of t, which is going to be negative 32 times t squared over 2, which that can simplify down to just 32 over 2.
00:30
One second here.
00:32
That's going to be, oh, that's obvious, negative 16 squared plus 4t, and then we would have a constant of integration, except for the fact that we know when t equals zero, h should be 400, so we just add on plus 400.
00:46
So that's for part a.
00:48
For part b, we're asked when the ballast will strike the ground, so we want to solve for t, such that negative 16t squared plus 4t plus 400 equals zero...