Question

Lesson: 3.03

Buffy and Addy launch their rockets at the same time. The height of Buffy's rocket, in
meters, is given by the function f x=-4.9x²+25x. where x is the number of seconds
after the launch. The height of Addy's rocket, in meters, is given by the function
g x=-4.9x² +16x+15 where x is the number of seconds after the launch. Algebraically
find the moment when the rockets are at the same height, and then use that to
calculate the height. Round to the nearest hundredth.

Answer 1

21.93 meters.

Explanation:

To find when the rockets are at the same height, we need to set the two functions equal to each other and solve for x:

-4.9x² + 25x = -4.9x² + 16x + 15

Simplifying this equation, we get:

9x = 15

x = 15/9

x ≈ 1.67

Therefore, the rockets are at the same height after approximately 1.67 seconds.

To find the height at which the rockets are at the same height, we can plug this value of x into either of the two functions. Let's use Buffy's function:

f(1.67) = -4.9(1.67)² + 25(1.67)

f(1.67) ≈ 21.93

Therefore, the height at which the rockets are at the same height is approximately 21.93 meters. Rounded to the nearest hundredth, this is 21.93 meters.