Question

A model rocket is fired from the ground at time t=0, and it’s height is given in cm by the formula h=-490t^2 +1470t where t is measured in seconds.

Write an equation to find when the height of the rocket is 980 cm.


Solve the equation by factoring.


Explain why there are two solutions to this problem.

Answer 1

Explanation:

h = -490t² + 1470t

When h = 980:

980 = -490t² + 1470t

Simplifying:

0 = -490t² + 1470t - 980

0 = t² - 3t + 2

Factoring:

0 = (t - 1) (t - 2)

t = 1, 2

There are two solutions because the rocket first reaches the height of 980 cm as it's going up at 1 second, then it reaches that height again as it's coming down at 2 seconds.