a model rocket is launched

Question

A model rocket is launched with an initial upward velocity of 57 m/s . The rocket's height h (in meters) after t seconds is given by the following.

h = 57t - 5t ^ 2

Find all values of for which the rocket's height is 29 meters.

Answer 1

h(t) = 57t - 5t², where t is time (in seconds) and h is the height (in meters).

We want to find the possible times for the rocket to reach at 29 feet. Set up the quadratic equation written in standard form.

29 = 57t - 5t² ⇒ 5t² - 57t + 29 = 0

Solve for t using the quadratic formula. Let a = 5, b = -57, and c = 29.

t = [-b ± √(b² - 4ac)] / 2a

t = [-(-57) ± √((-57)² - 4(5)(29)] / 2(5)

t = [57 ± √(3249 - 580)] / 10 ⇒ t = [57 ± √(2669)] / 10 ⇒ t = [57 ± √(2669)] / 10

t ≈ 0.5338 or t ≈ 10.8662

The rocket will reach 29 meters in height if it was launched either after 0.5338 seconds or 10.8662 seconds.