Ajuggler throws a ball from height of 0.950 m with an overall velocity of =4.25 m/s, 67 degrees above horizontal and misses it on the way down. What is the overall speed when it hits the ground?
The vertical velocity component starts out at
Vyo = 4.25 sin67 = 3.912 m/s
The horizontal velocity component remains constant until it hits the ground
Vxo = 4.25 cos67 = 1.661 m/s
Now use conservation of energy
Vyfinal^2 = Vyo^2 + 2 g H
= 33.92 m^2/s^2
Vyfinal = -5.824 m/s
The horizontal "component" of kinetic energy does not have to be included, since it does not change. The minus sign on velocity is becaus it is going down when it hits the ground.
Final overall speed = sqrt[(-5.824)^2 +(1.661)^2] = 6.057 m/s