Question

A rocket is fired into a country and has a flight path that can be modeled by the following equation:

h(t) = -5t^2 + 70
If the country’s radar can detect incoming rockets that are above 100 meters, after how many seconds will it detect the rocket? Give an exact answer (do not convert to a decimal).

Answer 1

To find when the radar detects the rocket above 100 meters using the given equation h(t) = -5t^2 + 70, solve for t by setting h(t) to 100, resulting in the exact time being the square root of 6 seconds.

Step-by-step explanation:

To determine after how many seconds the country's radar will detect a rocket above 100 meters, based on the given flight path equation h(t) = -5t^2 + 70, we need to solve for t when h(t) = 100. This involves setting the equation equal to 100 meters and solving for t:

100 = -5t^2 + 70

We then move 70 to the other side to isolate the quadratic term:

30 = -5t^2

Divide by -5 to solve for t^2:

-6 = t^2

Since the time cannot be negative, we take the square root, disregarding the negative solution:

t = √6

This gives us the exact time after which the radar will detect the rocket.