Question

analyzing projectile motion represented by a table the table relates to a function h(t) that models the height of a rock t seconds after it is dropped. t: 0, 0.5, 1, 1.5, 2, 2.5, 3 h(t): 20, 18.8, 15.1, 9, 0.4, -10.6, -24.1 when does the rock hit the ground? the rock hits the ground between seconds and seconds after it is dropped.

Explanation:

Step1: Analyze the sign of \( h(t) \)

We know that when the rock hits the ground, \( h(t) = 0 \). We need to find the interval where \( h(t) \) changes from positive to negative.
Looking at the table:

• At \( t = 2 \), \( h(2)=0.4 \) (positive)
• At \( t = 2.5 \), \( h(2.5)= - 10.6 \) (negative)

Step2: Determine the interval

Since \( h(t) \) is positive at \( t = 2 \) and negative at \( t = 2.5 \), by the Intermediate Value Theorem, the rock hits the ground (where \( h(t)=0 \)) between \( t = 2 \) seconds and \( t = 2.5 \) seconds.

Answer:

The rock hits the ground between 2 seconds and 2.5 seconds after it is dropped.