To find the velocity of the ball at a specific time, we must first find the velocity function. The velocity function is the derivative of the position function.
The position function for the ball is given by h(t) = -5t² + 30t + 2.
Taking the derivative of the position function with respect to time t, we obtain the velocity function.
The derivative of -5t² is -10t, the derivative of 30t is 30, and the derivative of a constant (2) is 0. So, the velocity function becomes v(t) = -10t + 30.
Now, plugging t=4s into the velocity function will give us the velocity of the ball at 4s.
That is, v(4) = -10(4) + 30 = -40 + 30 = -10 meters per second.
So, the velocity of the ball at t=4s is -10 m/s. This means that at 4 seconds the ball is moving downward at a rate of 10 meters per second.