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

Step-by-step 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.