Question

for a science experiment a projectile is launched. its path is given by H(d) =-5d^2+24d+30 where h is the the height of projectile above ground and d is the horizontal distance of the projectile from the launch pad both in metres. How far away from the pad was the projectile when it landed to the nearest tenth metre

Answer 1

The projectile will be about 5.8 meters away from the launch pad.

This is an example of a quadratic equation. Imagine a arch going up and then coming back down.

This is the path of the projectile. All we need to do is find the points when the arch is on the ground. In other words, when the equation is equal to zero.

You can do this with the quadratic equation. Just plug in A = -5, B = 24 and C = 30 and you will get the answers 5.8 and -1.

The negative answer doesn't make sense here, so the correct distance is 5.8.