Suppose a child drops a juice cup while in their high chair from a height of 3 feet. Use the position equation to determine how long it will take, in seconds, for the juice cup to hit the ground.

Answer 1

The height equation is:

h(t) = -16t² + v₀t + h₀

1. h(t) is the height at time t
2. t is time in seconds
3. v₀ is the initial (starting) velocity = 0 in this case since the child doesn't throw the object up or down (it just drops from rest)
4. h₀ is the initial height = 3 feet

Plugging in the initial values, we get:

h(t) = -16t² + 3

When the cup hits the ground, its height is zero; h(t) = 0:

0 = -16t² + 3

Solve for the time (t). You'll get two values, one positive and one negative. You want the positive value because we aren't going back in time. The units of t is seconds.