Step-by-step explanation:
Gravity on Earth is -32 ft/s². Gravity on the moon is 1/6 of that (-5.33 ft/s²).
The initial height is 6.5 ft, and the initial velocity is 40 ft/s.
So the height of the ball after t seconds is:
y = ½ a t² + v t + h
y = ½ (-5.33) t² + (40) t + (6.5)
y = -2.67t² + 40t + 6.5
When y = 18:
18 = -2.67t² + 40t + 6.5
2.67t² − 40t + 11.5 = 0
t = [ -(-40) ± √((-40)² − 4(2.67)(11.5)) ] / 2(2.67)
t = 0.293 or 14.707
The ball is 18 feet above the ground after 0.293 seconds and 14.707 seconds.
When y = 0:
0 = -2.67t² + 40t + 6.5
2.67t² − 40t − 6.5 = 0
t = [ -(-40) ± √((-40)² − 4(2.67)(-6.5)) ] / 2(2.67)
t = -0.161 or 15.161
t can't be negative, so the ball lands after 15.161 seconds.
