jmc

Question

Billy shoots an arrow from 10 feet above the ground. The height of this arrow can be expressed by the equation h=10-23t-10t^2, where t is time in seconds since the arrow was shot. If the center of a target is raised 5 feet off the ground, in how many seconds must the arrow reach the target in order for Billy to hit the bulls eye?

Accepted Answer

Since the center of the target is 5 feet above the ground, h=5. So we get the quadratic: align*5& =10-23t-10t^2 0& =10t^2+23t-5 0&=(2t+5)(5t-1). align*Thus, the values of t that satisfy the equation are -52 and 15. However, since time can never be a negative number, the answer must be 15.