With what speed should a body be thrown upwards so that the distance traversed in the 5th second and 6th second are equal?
49 m/s
Step 1: Given parameters
Time periods = 5 sec ad 6 sec
The acceleration due to gravity,
Step 2: Formula used
Use the first equation of motion given as
Where, is final velocity, is the initial velocity, is the acceleration due to gravity and is the time period.
Here, the acceleration due to gravity is negative as the body is moving up.
Step 3: Calculate the initial velocity
Consider the diagram illustrated below.
At 5th sec and 6th-sec, distance traveled = and in 4 sec to 5-sec, distance traveled =
Initially, the ball is thrown at a certain speed. We are supposed to find this speed.
The condition that distance traversed in 5th second and 6th seconds are equal only when the body is at the highest point, and it reaches there at the 5th second.
Here, the time of flight is equal to the time of descent. Hence the body is at its highest point at the 5th second.
This is only possible if the body decelerated in 4 seconds to 5 seconds and accelerated in 5 seconds to 6 seconds.
This condition is suited to projectile motion
In 4 sec to 5-sec body go upward and in 5 sec to 6-sec body go downward
Hence, at 5-sec body is at the top and its vertical velocity is zero.
Use the first equation of motion to calculate the initial velocity,
Hence, the initial velocity is 49 m/s.
Therefore, option (B) is correct.