Question

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

• A. \( 5 \, \text{m} \)
• B. \( 10 \, \text{m} \)
• C. \( 20 \, \text{m} \)
• D. \( 50 \, \text{m} \)

Hint:

Remember: At the highest point of a vertically thrown object, the final velocity is zero, which you can use to calculate the maximum height.

Answer 1

The Correct Option is A

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 \( u = 10 \, \text{m/s} \),
- Final velocity \( v = 0 \, \text{m/s} \) (since the object comes to rest at the highest point),
- \( g = 10 \, \text{m/s}^2 \).
Substitute these values into the equation: \[ 0 = (10)^2 - 2 \times 10 \times h \] \[ 0 = 100 - 20h \] \[ 20h = 100 \] \[ h = \frac{100}{20} = 5 \, \text{m} \] Answer: Therefore, the body will rise to a height of \( 5 \, \text{m} \). So, the correct answer is option (1).