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

The maximum height reached by the ball is about 20 meters, as determined by using the conservation of mechanical energy principle, considering that the total mechanical energy at the height of 10 meters was 100 Joules.

Step-by-step explanation:

To solve for the maximum height reached by the ball, we can use the conservation of mechanical energy principle, which states that the total mechanical energy (potential energy + kinetic energy) of the ball remains constant in the absence of air friction.

At 10 meters above the ground, the ball has a potential energy (PE) of 50 Joules and a kinetic energy (KE) of 50 Joules. Therefore, the total mechanical energy at that height is:

PE + KE = 50 J + 50 J = 100 J

As the ball rises, its kinetic energy is converted into potential energy until the kinetic energy becomes zero at the maximum height. The total mechanical energy at maximum height will be equal to the potential energy:

PE at maximum height = total mechanical energy = 100 J

Using the formula for gravitational potential energy, PE = mgh (where m is mass, g is the acceleration due to gravity (9.81 m/s²), and h is the height), and knowing that the PE at 10 meters is 50 J, we can find the mass of the ball:

50 J = m * 9.81 m/s² * 10 m

m = 50 J / (9.81 m/s² * 10 m) = 0.51 kg

With the mass of the ball, we can now calculate the maximum height using the total mechanical energy:

100 J = 0.51 kg * 9.81 m/s² * h

h = 100 J / (0.51 kg * 9.81 m/s²) ≈ 20 meters

Therefore, the maximum height h reached by the ball is about 20 meters.

Answer 2

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=(50)/(h)\\\\mg=(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=(100)/(5)\\\\h=20\ m`

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