Question

A ball is thrown upward from the ground. At a helght of 10 meters above the ground, the ball has a potential energy of 50 joules (with the potential eneray equal to zero at ground level) and is moving upward with a kinetic energy of 50 joules. Air friction is negligible. The maximum height above ground reached by the ball is most nearly

A. 10 m
B. 20m
C. 30 m
D. 40 m
E. 50 m

Answer 1

h = 20 m

Step-by-step explanation:

height (h) = 10 m

potential energy (PE) = 50 J

kinetic energy (KE) = 50 J

what is the maximum height reached by the ball

• At 10 meters above the ground potential energy (PE) = 50 J

mgh = 50

recall that height (h) = 10

mg (10) = 50

mg = 5 .....equation 1

• The total energy of the system at 10 meters is given as PE + KE = 100 Joules. From the conservation of energy the total energy in the system still remains the same at the maximum height, this is because energy can neither be created nor destroyed but can be transformed from one form to another.
• At the maximum height the velocity (v) of the system is 0, which means all its kinetic energy (KE) is converted to potential energy. Therefore the system consist only of potential energy.

KE + PE = 100

`0.5mv^(2)` + mgh = 100 J

velocity (v) = 0 at maximum height therefore

0 + mgh = 100

mgh = 100

recall that mg = 5 from equation 1, therefore

5h = 100

h = 20 m