The height (in feet) of a skydiver at time t (in seconds) after opening his parachute is given by h(t) = 4000 – 19t. Find the skydiver's velocity after the parachute opens. The answer should be in feet per seconds.
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To find the skydiver's velocity after the parachute opens, we need to calculate the derivative of the height function with respect to time.
Given that the height function is h(t) = 4000 – 19t, we can find its derivative by differentiating each term:
dh/dt = d(4000)/dt - d(19t)/dt
Since the derivative of a constant is zero, the first term simplifies to zero.
Now, let's differentiate the second term. The derivative of 19t with respect to t is simply 19.
Therefore, dh/dt = 0 - 19 = -19 ft/s
So, the skydiver's velocity after the parachute opens is -19 ft/s (negative because the skydiver is moving downward).