Question

A ball is thrown vertically upward with an initial velocity of \( 20 \, \text{m/s} \). Calculate the time taken for the ball to reach its maximum height.

• A. \( 2 \, \text{s} \)
• B. \( 4 \, \text{s} \)
• C. \( 1.5 \, \text{s} \)
• D. \( 3 \, \text{s} \)

Hint:

When solving problems involving vertical motion, always remember that gravity acts downward, so the acceleration will be negative when the object moves upward.

Answer 1

The Correct Option is A

We can use the first equation of motion to calculate the time taken to reach the maximum height: \[ v = u + at \] Where: - \( v = 0 \, \text{m/s} \) (final velocity at maximum height), - \( u = 20 \, \text{m/s} \) (initial velocity), - \( a = -9.8 \, \text{m/s}^2 \) (acceleration due to gravity, acting downward), - \( t \) is the time taken to reach maximum height. At maximum height, \( v = 0 \), so the equation becomes: \[ 0 = 20 + (-9.8) \times t \] Solving for \( t \): \[ t = \frac{20}{9.8} \approx 2.04 \, \text{s} \] Thus, the time taken for the ball to reach its maximum height is approximately \( 2 \, \text{s} \).