Question

A ball is thrown vertically upwards with an initial speed of 10 m/s. Calculate the maximum height reached by the ball. (Assume \( g = 9.8 \, \text{m/s}^2 \))

• A. \( 5 \, \text{m} \)
• B. \( 10 \, \text{m} \)
• C. \( 15 \, \text{m} \)
• D. \( 20 \, \text{m} \)

Hint:

To find the maximum height reached by a vertically thrown object, use the kinematic equation \( v^2 = u^2 - 2gh \), where \( v = 0 \) at the highest point.

Answer 1

The Correct Option is A

The initial velocity of the ball is given as \( u = 10 \, \text{m/s} \). At maximum height, the final velocity of the ball \( v = 0 \, \text{m/s} \), as it momentarily comes to rest before falling back down. Acceleration due to gravity is \( g = 9.8 \, \text{m/s}^2 \) (acting downward). We can use the following kinematic equation to find the maximum height: \[ v^2 = u^2 - 2gh \] Where: - \( v \) is the final velocity, - \( u \) is the initial velocity, - \( g \) is the acceleration due to gravity, - \( h \) is the height reached. Substituting the known values: \[ 0 = 10^2 - 2 \times 9.8 \times h \] \[ 100 = 19.6 \times h \] \[ h = \frac{100}{19.6} = 5.1 \, \text{m} \] Thus, the maximum height reached by the ball is approximately \( 5 \, \text{m} \).