Question

A ball is thrown vertically upwards with an initial velocity of $ 20 \, \text{m/s} $. How high will the ball rise? (Take $ g = 10 \, \text{m/s}^2 $)

• A. \( 20 \, \text{m} \)
• B. \( 40 \, \text{m} \)
• C. \( 10 \, \text{m} \)
• D. \( 25 \, \text{m} \)

Hint:

Remember: At the highest point, the final velocity of an object thrown vertically upwards is zero. Use this to calculate the maximum height.

Answer 1

The Correct Option is B

Step 1: Use the equation of motion for vertical displacement
The height reached by an object thrown vertically upwards can be calculated using the following equation of motion: \[ v^2 = u^2 - 2gh \] 
where: 
- \( v \) is the final velocity (which is 0 at the highest point), 
- \( u \) is the initial velocity, 
- \( g \) is the acceleration due to gravity, 
- \( h \) is the maximum height. 
Step 2: Substitute the given values
Given: - Initial velocity \( u = 20 \, \text{m/s} \), 
- Final velocity \( v = 0 \, \text{m/s} \) (since the ball comes to rest at the highest point), - \( g = 10 \, \text{m/s}^2 \). 
Substitute these values into the equation: \[ 0 = (20)^2 - 2 \times 10 \times h \] \[ 0 = 400 - 20h \] \[ 20h = 400 \] \[ h = \frac{400}{20} = 20 \, \text{m} \] 
Answer:
Therefore, the ball will rise to a height of \( 40 \, \text{m} \). So, the correct answer is option (2).