Question

A 0.2 kg ball is thrown vertically upwards with an initial velocity of \( 10 \, \text{m/s} \). What is the maximum height reached by the ball? (Acceleration due to gravity \( g = 9.8 \, \text{m/s}^2 \))

• A. \( 5 \, \text{m} \)
• B. \( 10 \, \text{m} \)
• C. \( 20 \, \text{m} \)
• D. \( 2 \, \text{m} \)

Hint:

When an object is thrown upwards, use the kinematic equation \( v^2 = u^2 - 2gh \) to find the maximum height. At the maximum height, the final velocity is zero.

Answer 1

The Correct Option is A

Step 1: Use the kinematic equation to find the maximum height At the maximum height, the final velocity \( v = 0 \, \text{m/s} \). The equation for vertical motion is: \[ v^2 = u^2 - 2 g h \] Where: - \( v \) is the final velocity - \( u \) is the initial velocity - \( g \) is the acceleration due to gravity - \( h \) is the maximum height Given: - \( u = 10 \, \text{m/s} \) - \( v = 0 \, \text{m/s} \) - \( g = 9.8 \, \text{m/s}^2 \) Rearrange the formula to solve for height \( h \): \[ 0 = (10)^2 - 2 \times 9.8 \times h \] \[ h = \frac{(10)^2}{2 \times 9.8} = \frac{100}{19.6} \approx 5 \, \text{m} \] Answer: Therefore, the maximum height reached by the ball is \( 5 \, \text{m} \). So, the correct answer is option (1).