(a) The vertical motion equation for the ball is h = 8 + 48t - 16t².
(b) The time for the ball to hit the ground is 3.15 s.
(c) The time for the ball to travel 56 ft above the ground is 0.79 s.
Vertical motion equation for the ball
The vertical motion equation for the ball is calculated as follows;
h = h₀ + vt - ¹/₂gt²
h = 8 + 48t - ¹/₂(32)t²
h = 8 + 48t - 16t²
Time for the ball to hit the ground
0 = 8 + 48t - 16t²
solve the above quadratic equation with formula method;
a = -16, b = 48, c = 8
t = 3.15 s
Time for the ball to be 56 ft above the ground
- let upward motion be positive
h = 8 + 48t + 16t²
56 = 8 + 48t + 16t²
0 = -48 + 48t + 16t²
solve the above quadratic equation with formula method;
a = 16, b = 48, c = -48
t = 0.79 s
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