Answer:
Height = 555 meters
Time = 15 seconds
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.
