Question

The height of an object above the ground in feet can be modeled as a function of time, t, in seconds using the equation: h(t)= -16(t-3)^2 + 288 for t grater than or equal to 0. a)Find the time in seconds when the object reaches the ground (h=0). Round your answer to the nearest second. Hint- Solve by taking the square root. b) Find all times when the object is at a height of 150 feet. Round your answer to the nearest second. Hint-Solve by taking the square root.)

Answer 1

(a) t = 7 sec approximately; (b) t = 6 sec

Explanation:

(a) Set h(t)= -16(t-3)^2 + 288 = 0 and solve for t:

16(t-3)^2 = 288

After simplification, this becomes (t - 3)^2 = 18, or t - 3 = ±3√2.

Because t can be only zero or positive, t = 3 + 3√2 = 7 seconds

(b) Solve h(t)= -16(t-3)^2 + 288 = 150:

-16(t-3)^2 = - 162

or (t - 3)^2 = 10.125, or

t - 3 = ±3.18, or, finally, t = 6.18 sec (discard t = -0.18 sec)