Calculating Time Taken for a Ball to Reach Maximum Height

Question:

What is the time taken for a ball to reach its maximum height when thrown vertically upwards with a velocity of 10 m/s from a balcony 15m above the ground?

Answer:

The time taken for the ball to reach its maximum height is 1 second.

Calculating Time Taken for a Ball to Reach Maximum Height

When a ball is thrown vertically upwards from a height of 15m above the ground with an initial velocity of 10 m/s, we can calculate the time taken for the ball to reach its maximum height using kinematic equations for vertical motion.

Kinematic Equation:

v = u + at

Where:

v = final velocity

u = initial velocity

a = acceleration

t = time

In this case, the initial velocity (u) is 10 m/s (considering upwards as positive) and the acceleration (a) is -10 m/s² (negative because it opposes the motion). At the maximum height, the final velocity (v) will be zero as the ball momentarily comes to a stop before changing direction.

Using the kinematic equation:

0 = 10 - 10t

Solving for time (t):

10t = 10

t = 1 second

Therefore, the time taken for the ball to reach its maximum height is 1 second. During this time, the ball overcomes gravitational acceleration to reach its peak height, before descending back towards the ground due to gravity.