Question

A ball is thrown vertically upwards with a speed of \( 20 \, \text{m/s} \). What is the maximum height reached by the ball? Assume the acceleration due to gravity is \( g = 9.8 \, \text{m/s}^2 \).

• A. \( 20.4 \, \text{m} \)
• B. \( 40.8 \, \text{m} \)
• C. \( 10.2 \, \text{m} \)
• D. \( 50.4 \, \text{m} \)

Hint:

To find the maximum height in vertical motion, use the equation \( v^2 = u^2 + 2as \) where the final velocity \( v = 0 \) at the highest point.

Answer 1

The Correct Option is A

Step 1: Understand the given data. - Initial velocity of the ball, \( u = 20 \, \text{m/s} \) - Final velocity at maximum height, \( v = 0 \, \text{m/s} \) (since the ball comes to rest at the highest point) - Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \) (acting downward, so we take \( a = -9.8 \, \text{m/s}^2 \)) Step 2: Use the second equation of motion. The second equation of motion relates initial velocity, final velocity, acceleration, and displacement (which in this case is the maximum height): \[ v^2 = u^2 + 2a s \] Substitute the known values: \[ 0 = (20)^2 + 2 \times (-9.8) \times s \] \[ 0 = 400 - 19.6s \] \[ 19.6s = 400 \] \[ s = \frac{400}{19.6} \approx 20.4 \, \text{m} \] Answer: Therefore, the maximum height reached by the ball is \( 20.4 \, \text{m} \).