Question

h = -15 sin (π/7 (t-2)) + 42

h is the height of the ball above the floors in inches at time t seconds

1) what is the highest the ball will ever bounce?
2) when is the first time the ball bounces that high?
3) write a general expression for the times at which the ball is at its highest point.

Answer 1

(1) surely you know that the maximum value of sin() is 1. So, 15+42 is the max for h

(2) you want sin (π/7 (t-2)) to be -1, so
(π/7 (t-2)) = 3π/2
t=25/2

(3) since the period is 2π/(π/7) = 14, the max will occur at 25/2 + 14k for integer values of k.

The above assertions can be seen on the graph at

http://www.wolframalpha.com/input/?i=-15+sin+%28%CF%80%2F7+%28t-2%29%29+%2B+42+for+0%3C%3Dt%3C%3D20