Question

A rocket is fired directly upwards with a velocity of 80 ft/sec. The equation for its height, H, as a function of time, t, is

given by the function
H (t) = -1612 + 80+
Find the time at which the rocket reaches its maximum height, and its maximum height.
5
a) O time =
22
sec, max height = 200 ft
b) O time = 80 sec, max height = 100 ft
5
c) O time =
2
sec, max height = 100 ft
d) O time = 5 sec, max height = 200 ft
5
e) Otime = sec, max height = 400 ft
23
Revie

Answer 1

The time at which the rocket reaches its maximum height is 2.5 seconds and the maximum height reached by the rocket is -1512 feet.

Step-by-step explanation:

The maximum height reached by a rocket fired directly upwards can be determined using the equation H(t) = -1612 + 80t - 16t^2, where H(t) represents the height of the rocket at time t. To find the time at which the rocket reaches its maximum height, we need to find the vertex of the parabolic function. The time at which the rocket reaches its maximum height is given by the formula t = -b/2a, where a = -16 and b = 80. Substituting the values, we get t = -80/(2*-16) = 2.5 seconds. Therefore, the time at which the rocket reaches its maximum height is 2.5 seconds.

To find the maximum height of the rocket, we substitute the value of t from above into the equation H(t). H(2.5) = -1612 + 80*2.5 - 16*(2.5)^2 = -1612 + 200 - 100 = -1512. Therefore, the maximum height reached by the rocket is -1512 feet.

Answer 2

(c).

Step-by-step explanation:

h(t) = - 16 t² + 80 t

Coordinates of the vertex are:

t = -
`(80)/(2(-16))` =
`(5)/(2)` = 2.5 sec.

h = - 16(2.5)² + 80(2.5) = - 100 + 200 = 100 ft.