Question

A tourist jumps off a 64-foot cliff to swim with pink river dolphins in Bolivia. The tourist's height in feet above the water is modeled by h(t) = -16t^2 + 64, where t is the time in seconds after the tourist jumps from the cliff. About how long will it take the tourist to reach the water?

a) 2 seconds
b) 4 seconds
c) 8 seconds
d) 16 seconds

Answer 1

To determine the time it takes for the tourist to hit the water, we set the height equation h(t) to zero and solve for t, finding that it will take approximately 2 seconds.

Step-by-step explanation:

The tourist's height above the water after jumping from the cliff is modeled by the equation h(t) = -16t^2 + 64. To find out how long it will take the tourist to reach the water, we need to set h(t) to 0 and solve for t. That is because the height above the water will be 0 when the tourist hits the water.

Setting h(t) to 0, we get:

• 0 = -16t^2 + 64
• 16t^2 = 64
• t^2 = 64 / 16
• t^2 = 4
• t = √4
• t = 2 seconds

Therefore, the tourist will take about 2 seconds to reach the water.