How can I figure this problem out?

Question

So my problem on my precalculus homework is “Rodney shoots a basket at 6.5ft above the ground. It’s initial velocity is 25 feet per second. How many seconds after shooting does the ball go through the hoop?”

 

im so confused

Answer 1

We need to know the height of the hoop, which the problem statement does not provide. Suppose it is H (in feet). Assuming the ball is tossed vertically up (another detail that is missing from the problem statement), the height h as a function of time t is

h(t) = (-1/2)32t² + 25t + 6.5 = -16t² + 25t + 6.5

h in feet, t in seconds

When it reaches a height H,

H = -16t² + 25t + 6.5

-16t² + 25t + (6.5 - H) = 0

Solve this quadratic equation for t. I should give a negative and a positive solution, Since t starts at t = 0, the answer is the positive solution. Plug in the correct value of H and solve.