(a) 134.4 J
The total mechanical energy of the ball at the moment of launch is just equal to its initial kinetic energy:
where
m = 0.05 kg is the mass of the ball
u = 78.2 m/s is the initial speed
Substituting,
At the pinnacle of its trajectory, the total mechanical energy is sum of kinetic energy and potential energy:
where
is the acceleration of gravity
h = 37.8 m is the maximum height
Since the total energy must be conserved,
E = 152.9 J
Therefore, we can solve to find the kinetic energy of the ball at the pinnacle:
b) 74.2 m/s
When the ball is 5.60 m below the pinnacle point, the heigth of the ball is
So its potential energy is
The total energy is again the sum of potential and kinetic energy:
E = K + U
So the kinetic energy at that point is
And since the kinetic energy is
We can find the speed: