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: Apply vertical displacement kinematic equation
The maximum height of an object projected vertically upwards is determined by: \[v^2 = u^2 - 2gh\]where:
- \( v \) denotes the final velocity (zero at peak altitude),
- \( u \) is the initial velocity,
- \( g \) represents the acceleration due to gravity,
- \( h \) signifies the maximum height.
Step 2: Input given data
Given:
- Initial velocity \( u = 10 \, \text{m/s} \),
- Final velocity \( v = 0 \, \text{m/s} \) (object is momentarily stationary at its highest point),
- Gravitational acceleration \( g = 10 \, \text{m/s}^2 \).
Substituting these into the equation yields:\[0 = (10)^2 - 2 \times 10 \times h\]\[0 = 100 - 20h\]\[20h = 100\]\[h = \frac{100}{20} = 5 \, \text{m}\]Conclusion: The object will reach an altitude of \( 5 \, \text{m} \). The correct option is (1).