Answer:
10.9 m
Explanation:
We can solve the problem by using the law of conservation of energy.
The initial mechanical energy is just the kinetic energy of the ball:
[tex]E = K_i = \frac{1}{2}mu^2[/tex]
where m is the mass of the ball and u = 16.9 m/s the initial speed.
At a height of h, the total mechanical energy is sum of kinetic energy and gravitational potential energy:
[tex]E=K_f + U_f = \frac{1}{2}mv^2 + mgh[/tex]
where v is the new speed, g is the gravitational acceleration, h is the height of the ball.
Due to the conservation of energy,
[tex]\frac{1}{2}mu^2 = \frac{1}{2}mv^2 +mgh\\u^2 = v^2 + 2gh[/tex] (1)
Here, at a height of h we want the speed to be 1/2 of the initial speed, so
[tex]v=\frac{1}{2}u[/tex]
So (1) becomes
[tex]u^2 = (\frac{u}{2})^2+2gh\\\frac{3}{4}u^2 = 2gh[/tex]
So we can find h:
[tex]h=\frac{3u^2}{8g}=\frac{3(16.9 m/s)^2}{8(9.8 m/s^2)}=10.9 m[/tex]
