Physics 2022 JAMB Past Questions - Question 5: A 1.5kg stone was thrown vertically upward with an initial velocity of 42m/s, What is the potential energy of the stone at the highest point reached.

Correct Answer

B

Explanation

To find the potential energy of the stone at the highest point reached, we can use the formula for gravitational potential energy:

\[ PE = mgh \]

Where:
- \( m = 1.5 \, \text{kg} \) (mass of the stone)
- \( g = 9.81 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h \) is the height at the highest point reached, which can be found using the kinematic equation:

\[ v_f^2 = v_i^2 + 2gh \]

Where:
- \( v_f = 0 \, \text{m/s} \) (final velocity at the highest point, when the stone momentarily stops before falling back down)
- \( v_i = 42 \, \text{m/s} \) (initial velocity)
- \( g = 9.81 \, \text{m/s}^2 \) (acceleration due to gravity)

First, we can find the height \( h \) using the kinematic equation:

\[ 0 = (42 \, \text{m/s})^2 + 2(-9.81 \, \text{m/s}^2)h \]

Solving for \( h \), we get:

\[ h = \frac{(42 \, \text{m/s})^2}{2 \times 9.81 \, \text{m/s}^2} \]

\[ h \approx 90.92 \, \text{m} \]

Now that we have the height, we can find the potential energy:

\[ PE = (1.5 \, \text{kg}) \times (9.81 \, \text{m/s}^2) \times (90.92 \, \text{m}) \]

\[ PE \approx 1330.5 \, \text{J} \]

So, the potential energy of the stone at the highest point reached is approximately 1330.5 joules.