We have given the maximum vertical height attained by the object is h=10m .
(a)To calculate the initial velocity of the object with which it is thrown upward,
Where, v is the final velocity, u is the initial velocity, g is the gravitational acceleration, and h is the object’s height. We know that when an item reaches its maximum height, its velocity becomes zero.
We know that at the maximum height, the velocity of the object becomes zero.
Therefore, we can substitute 0 for v in the above equation. 02 = u2 −2gh
⇒ u2 = 2gh ⇒ u =√2gh
Substituting 9.8m/s2 for g and 10 m for h in the above equation,
we get, u = √2(9.8)(10)
Therefore, the initial velocity of the object is 14 m/s.
(b) To calculate the time taken by the object to reach the height h,
we can use following kinematic equation, v=u−gt
Since final velocity v is zero, the above equation becomes, u=gt
⇒ t = ug
Substituting 14 m/s for u and 9.8m/s2 for g in the above equation, we get, t=149.8
Therefore, the time taken by the object to reach the highest point is 1.43 seconds.