Question

A ball is thrown upward. At a height of 10 meters above the ground, the ball has a potential energy of 50 Joules (with the potential energy equal to zero at ground level) and is moving upward with a kinetic energy of 50 Joules. What is the maximum height h reached by the ball? Consider air friction to be negligible.

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

Answer 1

Given that,

A ball is thrown upward. At a height of 10 meters above the ground, the ball has a potential energy of 50 Joules. It is moving upward with a kinetic energy of 50 Joules.

We need to find the maximum height h reached by the ball. Let at a height of 10 meters, it has a potential energy of 50 Joules. So,

$mgH=50\\\\mg=\dfrac{50}{h}\\\\mg=\dfrac{50}{10}\\\\mg=5\ N$ ........(1)

Let at a height of h m, it reaches to a maximum height. at this point, it has a total of 100 J of energy. So,

$mgh=50+50\\\\mgh=100\\\\h=\dfrac{100}{5}\\\\h=20\ m$

So, the correct option is (E) "h = 20 m".