Answer:
For first part, t= 0.18 sec or 3.4 sec.
For second part, t= 3.7 sec.
Step by step answer:
First part:
Set h(t) = 17and solve for tt.
-16t²+ 58t + 7= 17
-16t² + 58t - 10 = 0
Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 17 on the way up, and the higher value is the time to reach 17 again, on the way down.
Second part:
Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.
