A model rocket is launched with an initial upward velocity of 62 m/s The rocket's height h (in meters) after t seconds is given by the following.
h=62t-5t^2
Find all values of t for which the rocket's height is 29 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
To find the values of t for which the rocket's height is 29 meters, we set h equal to 29 and solve for t.
29 = 62t - 5t^2
5t^2 - 62t + 29 = 0
This is a quadratic equation that we can solve using the quadratic formula:
t = [-(-62) ± √((-62)^2 - 4*5*29)] / 2*5
t = [62 ± √(3844 - 580)] / 10
t = [62 ± √3264] / 10
t = [62 ± 57.14] / 10
So, the values of t for which the rocket's height is 29 meters are:
t ≈ 11.86 or t ≈ 1.14