Question

Write a vertical motion model in the form h(t)=-16t^2+v0^2+h0 for each situation presented. For each situation, determine how long, in seconds, it takes the thrown object to reach maximum height.

Initial velocity: 120 ft/s; initial height: 50 ft

Answer 1

-16t^2 + 120t + 50

Explanation:

Using the given values, we can write the model for this situation as:

h(t) = -16t^2 + 120t + 50

To determine how long it takes the thrown object to reach maximum height, we need to find the time at which the object reaches its maximum height. The maximum height occurs at the vertex of the parabolic path, which is given by:

t = -b / 2a

where a = -16, b = 120.

Substituting these values, we get:

t = -120 / 2(-16) = 3.75 seconds

Therefore, it takes 3.75 seconds for the thrown object to reach maximum height.