Question

A potato is launched vertically upward with an initial velocity of 100 ft/s from a potato gun at the top of a 75 ft tall building. The distance, in feet, that the potato travels from the ground after t seconds is given by s(t) = -16t² + 100t + 75.

Find the velocity of the potato (in ft/s) after 0.75 s and 5.5 s.
velocity at 0.75 s ________ ft/s
velocity at 5.5 s _________ ft/s

Answer 1

The velocity of the potato at 0.75 seconds is 76 ft/s upwards, and at 5.5 seconds, it is 76 ft/s downwards.

Step-by-step explanation:

To find the velocity of the potato at given times after launch, we need to take the derivative of the position function s(t) to get the velocity function v(t).

The given position function is s(t) = -16t² + 100t + 75. The velocity function v(t) is the first derivative of the position function with respect to time:

v(t) = s'(t) = -32t + 100.

We can now calculate the velocity at t = 0.75 s and t = 5.5 s using the velocity function:

• Velocity at 0.75 s: v(0.75) = -32(0.75) + 100 = -24 + 100 = 76 ft/s
• Velocity at 5.5 s: v(5.5) = -32(5.5) + 100 = -176 + 100 = -76 ft/s

The negative velocity at 5.5 s indicates the potato is moving downwards at that time.