Question

A potato launched by a particular potato gun has a height described by h(t) = 16t^2 + 152t + 2. When is the potato 282 feet in the air?

a. 1.5 seconds on the way up and 2.5 seconds on the way back down.
b. 2 seconds on the way up and 3 seconds on the way back down.
c. 3 seconds on the way up and 4 seconds on the way back down.
d. 4.5 seconds on the way up and 5.5 seconds on the way back down.

Answer 1

The potato is 282 feet in the air at 1.5 seconds on the way up and 2.5 seconds on the way back down.

Step-by-step explanation:

To determine when the potato is 282 feet in the air, we need to set the height equation equal to 282 and solve for t:

282 = 16t^2 + 152t + 2

Simplifying the equation, we get:

16t^2 + 152t - 280 = 0

Using the quadratic formula, we find two solutions: t = -8.5 seconds and t = 1.5 seconds. Since time cannot be negative, the potato is 282 feet in the air at t = 1.5 seconds on the way up. It will then be 282 feet in the air again on the way down at t = 2.5 seconds. Therefore, the correct answer is (a) 1.5 seconds on the way up and 2.5 seconds on the way back down.