Question

The function h defined by h() = (37 + 5)(15 − ) models the height, in meters, of an object seconds after it is dropped from a helicopter.From what height is the object dropped? Explain or show your reasoning.

Answer 1

Height = 555 meters

Time = 15 seconds

Step-by-step explanation:

The object is dropped at t = 0 seconds, so to know the answer, we need to find the height at t = 0.

Therefore, replacing t by 0 on the equation of h(t), we get:

h(t) = (37 + 5t)(15 - t)

h(0) = (37 + 5(0))(15 - 0)

h(0) = (37 + 0)(15 - 0)

h(0) = (37)(15)

h(0) = 555

So, the object is dropped from 555 meters

On the other hand, the object hits the ground when its height is equal to 0 m, so to approximate the time when the object hits the ground, we need to solve the following equation:

(37 + 5t)(15 - t) = 0

Now, a product is equal to 0 if at least one of the factors is equal to zero. It means that the possible solutions for the equation are:

37 + 5t = 0

37 + 5t - 37 = 0 - 37

5t = -37

5t/5 = -37/5

t = -7.4

or

15 - t =0

15 - t + t = 0 + t

15 = t

t = 15

Since t = -7.4 seconds doesn't have sense here, the correct solution is t = 15 seconds.

Therefore, the object hits the ground at t = 15 seconds.