Question

Brynn and Denise launch their rockets at the same time. The height of Brynn’s rocket, in meters, is given by the function f(x)=−4.9x^2+75x , where x is the number of seconds after the launch.
The height of Denise’s rocket, in meters, is given by the function g(x)=−4.9x^2+50x+38 , where x is the number of seconds after the launch.

There is a moment when the rockets are at the same height.



What is this height rounded to the nearest tenth of a meter?

Answer 1

-4.9x²+75x=-4.9x+50x+38
75x=50x+38
25x=38
x=1.52
1.52 minutes after launching, the height is: -4.9(1.52)²+75(1.52)=102.67904≈102.7 meters
Double check: -4.9(1.52)²+50(1.52)+38=102.67904≈102.7. Yes.
so the height is 102.7 meter.