Answer:
Speed of the ball when it was thrown = 16.67 m/s
Height reached by the ball = 14.16 s
Explanation:
Given time in the ball comes to the same height from where the ball was thrown is 3.4 s.
Let us assume that the ball was thrown with a speed of u in the upward direction. Since only gravitational force acts on the particle in the downward direction, it has a constant acceleration in the downward direction.
We also know that a particle has the same magnitude of velocity when it is under a free fall at a fixed height but direction is opposite i.e., initially in the upward direction and finally in the downward direction.
https://tex.z-dn.net/?f=%5Ctherefore%20%5Cdfrac%7B-u-u%7D%7B3.4%7D%3D%20-9.8%5C%5C%5CRightarrow%20%5Cdfrac%7B2u%7D%7B3.4%7D%3D%209.8%5C%5C%5CRightarrow%202u%20%3D%209.8%5Ctimes%203.4%5C%5C%5CRightarrow%20u%20%3D%20%5Cdfrac%7B9.8%5Ctimes%203.4%7D%7B2%7D%5C%5C%5CRightarrow%20u%20%3D%2016.67%5C%20m%2Fs
Hence, the particle was thrown with a speed of 16.67 m/s.
Now, we also note that the particle has zero velocity at its maximum height.
So, from the initial position to the maximum height reached by the particle, we have
https://tex.z-dn.net/?f=0%5E2%20%3D%20u%5E2%2B2as%5C%5C%5CRightarrow%20s%20%3D%20%5Cdfrac%7Bv%5E2-u%5E2%7D%7B2a%7D%5C%5C%5CRightarrow%20s%20%3D%20%5Cdfrac%7B0%5E2-16.67%5E2%7D%7B2(-9.8)%7D%5C%5C%5CRightarrow%20s%20%3D14.16%5C%20m
Hence, the maximum height reached by the ball is 14.16 m.
