Question

A model rocket is launched with an initial upward velocity of 62/ms. 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.

Answer 1

9514 1404 393

Answer:

t = 0.49, 11.91

Explanation:

A graphing calculator can show you the answers quickly. The times are 0.49 seconds and 11.91 seconds.

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We can write the equation as ...

h = 29

62t -5t^2 = 29 . . . . . substitute for h

-5(t^2 -12.4t) = 29

-5(t^2 -12.4t +6.2^2) = 29 -5(6.2^2) . . . . complete the square

-5(t -6.2)^2 = -163.2 . . . . . simplify

t -6.2 = ±√(-163.2/-5) = ±√32.64 . . . . divide by -5, take the square root

t = 6.2 ±5.71

t = 0.49, 11.91

The rocket has a height of 29 meters at t=0.49 seconds and t=11.91 seconds.