Question

A town launches fireworks from the top of city hall to celebrate the Fourth of July. The height h(t) of the fire-works (in meters above the ground) can be calculated using the function h(t) = -4.9t 2+ 140t + 15, where t is the time in seconds. 4. What is the maximum height that the fireworks will reach?

Answer 1

1,015 m

Explanation:

The maximum height is obtained at the value of t when dh(t)/dt = 0. So, differentiating h(t) with respect to t, we have

h(t) = -4.9t² + 140t + 15

d[h(t)]/dt = d[-4.9t² + 140t + 15]/dt

d[h(t)]/dt = -9.8t + 140

equating d[h(t)]/dt = 0, we have

-9.8t + 140 = 0

-9.8t = -140

t = -140/-9.8

t = 14.29 s

So, substituting t = 14.29 into h(t), we have

h(t) = -4.9t² + 140t + 15

h(14.29) = -4.9(14.29)² + 140(14.29) + 15

= -1000.6 + 2000.6 + 15

= 1000 + 15

= 1,015 m