Physics and I just don't seem to get along this week....?

Question

A dolphin jumps with an initial velocity of 11.5 m/s at an angle of 40.0° above the horizontal. The dolphin passes through the center of a hoop before returning to the water. If the dolphin is moving horizontally when it goes through the hoop, how high above the water is the center of the hoop?

Answer 1

Based on the givens, the vertical velocity is zero at the center of the hoop, therefore
0=11.5*sin(40)-g*t
solve for t and plug into
y(t)=11.5*sin(40)*t-.5*g*t^2

you will find that
y(t)=.5*11.5^2*sin^2(40)/g

2.785 meters

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