A rocket is launched vertically from the ground with an initial velocity of 56 ft/sec

(a) Write a quadratic function that shows the height, in feet, of the rocket t seconds after it was launched.

(b) Graph on the coordinate plane.

(c) Use your graph from Part 3 (b) to determine the rocket's maximum height, the amount of time it took to reach its maximum height, and the amount of time it was in the air.

Question

Mohammed Mayer

Mathematics

25 July, 19:41

A rocket is launched vertically from the ground with an initial velocity of 56 ft/sec

(a) Write a quadratic function that shows the height, in feet, of the rocket t seconds after it was launched.

(b) Graph on the coordinate plane.

(c) Use your graph from Part 3 (b) to determine the rocket's maximum height, the amount of time it took to reach its maximum height, and the amount of time it was in the air.

+5

Answers (1)

Know the Answer?

Marcel Yang · Answer 1

y = 17x - 4.5x²

height = 16m at 2 sec

total time = 3.77 sec

Step-by-step explanation:

Given the initial velocity of rocket = 56ft/sec

We use newton formula

s = ut + 1/2at²where s = distance

u = initial velocity

t = time

a = acceleration due to gravity = 9.8m/s²

since the rocket is launched upward, it is against the gravity so a = - 9.81.

56 feet = 17.0688 = 17

suppose s = height = y and time = x

y = 17x - 1/2 (9.81) x²

or

y = 17x - 4.5x²

b)

as x can not be negative so domain will be from 0 to 3.78

put value of x to find value of y and then plot these on graph

This graphs will be a parabola which opens downward.

c)

at 2 sec, y value is greatest = 16 meters

time for which rocket was in the air = 3.77sec