Final answer:
By using the kinematic equation v = vo + at, and setting vo to 0 m/s and a to -9.81 m/s² (acceleration due to gravity), the time t required for a dropped pumpkin to reach a velocity of -18 m/s is calculated by dividing -18 m/s by -9.81 m/s².
Step-by-step explanation:
To find the time required for a rotten pumpkin to reach a velocity of -18 m/s when dropped off a cliff, we use the kinematic equation v = vo + at. Here, v is the final velocity, vo is the initial velocity, a is the acceleration due to gravity, and t is the time.
Given that the initial velocity (vo) is 0 m/s (since the pumpkin is dropped and not thrown) and the acceleration due to gravity (a) is approximately -9.81 m/s² (negative because it's directed downwards), we can rearrange the equation to solve for time (t).
So v = -18 m/s (negative sign indicating direction downwards), vo = 0 m/s, and a = -9.81 m/s².
Plugging these values into the formula gives: -18 m/s = 0 m/s + (-9.81 m/s²)*t
To find t, divide both sides by -9.81 m/s²: t = (-18 m/s) / (-9.81 m/s²).
Doing the calculation provides the time required for the pumpkin to reach -18 m/s.