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.