00:01
In this case, you want to find out the boat's velocity at the half of the maximum height relative to equilibrium point of the spring.
00:07
So in this case, we know that at equilibrium point, the total energy, e total, equals one -half kd -square.
00:21
K is the spring constant.
00:23
D is the spring compression.
00:25
Now, when a ball leaves the spring, it has the maximum kinetic energy.
00:30
And no gravitational potential energy.
00:35
But at the maximum height, so the first one is at the equilibrium, and then half of the maximum height.
01:01
Now the total energy of the ball is split between the gravitational potential energy because it has a gravity.
01:07
So this is p, potential energy, gravitational potential energy, equals the mass multiplied by the gravitational acceleration and half of the height.
01:21
Then the other part is the kinetic energy.
01:24
Kinetic energy is going to be one half multiplied by the mass, multiplied by v squared.
01:34
V0 .5 square is the velocity, especially at the half of the maximum height.
01:45
Now we can say that combine these two, e total energy, one -half kd squared equals 1 .5m times v0 .5 square plus mg, half, h divided by 2.
02:07
And you can actually rearrange it...