Answer:
h = 31.9 m
Step-by-step explanation:
Since, the ball took 5.1 s in the air. Hence, the time to reach maximum height will be equal to the half of this value:
t = 5.1 s /2 = 2.55 s
Now, we use 1st equation of motion between the time of throwing and the time of reaching maximum height:
Vf = Vi + gt
where,
Vf = Final Velocity = 0 m/s (since, ball momentarily stops at highest point)
Vi = Initial Velocity = ?
g = - 9.8 m/s² (negative sign for upward motion)
Therefore,
0 m/s = Vi + (-9.8 m/s²)(2.55 s)
Vi = 24.99 m/s
Now, we use second equation of motion for height (h):
h = Vi t + (0.5)gt²
h = (24.99 m/s)(2.55 s) + (0.5)(-9.8 m/s²)(2.55 s)²
h = 63.7 m - 31.8 m
h = 31.9 m