Question

A particle is projected vertically upward with an initial velocity of $ 20 \, m/s $. Calculate the maximum height reached by the particle.

• A. \(20 \, m\)
• B. \(15 \, m\)
• C. \(10 \, m\)
• D. \(25 \, m\)

Hint:

Tip: At maximum height, velocity becomes zero. Use appropriate kinematic formulas accordingly.

Answer 1

The Correct Option is A

Step 1: Write down known variables 
Initial velocity, \( u = 20 \, m/s \)
Final velocity at maximum height, \( v = 0 \, m/s \)
Acceleration due to gravity, \( g = 9.8 \, m/s^2 \) (downward)

Step 2: Use kinematic equation 
\[ v^2 = u^2 - 2gh \] where \( h \) is the maximum height.

Step 3: Substitute values and solve for \( h \) 
\[ 0 = (20)^2 - 2 \times 9.8 \times h \implies 400 = 19.6h \implies h = \frac{400}{19.6} \approx 20.41 \, m \]

Step 4: Final answer 
Rounded to nearest option: \( h = 20 \, m \).