Answer:
50.0 m
Explanation:
First of all, we can find the initial velocity of the ball, using the equation
v = u + at
where
v = 0 is the velocity of the ball at the highest position
u is the initial velocity
[tex]a=g=-9.8 m/s^2[/tex] is the acceleration of gravity
[tex]t=\frac{6.37}{2}=3.19 s[/tex] is the time the ball took to reach the maximum height (half of the time it remained in the air)
Solving for u,
[tex]u=v-at=0-(-9.8)(3.19)=31.3 m/s[/tex]
Now we can find the maximum height using the other SUVAT equation:
[tex]v^2-u^2 = 2ad[/tex]
where d is the maximum height. Solving for d,
[tex]d=\frac{v^2-u^2}{2a}=\frac{0^2-(31.3)^2}{2(-9.8)}=50.0 m[/tex]
