Correct Answer - Option 3 : Both a and b are correct
CONCEPT:
Equation of Kinematics:
- These are the various relations between U, V, a, t, and s for the particle moving with uniform acceleration where the notations are used as:
- Equations of motion can be written as
⇒ V = U + at
\(⇒ s =Ut+\frac{1}{2}{at^{2}}\)
⇒ V2 = U2+ 2as
where, U = Initial velocity, V = Final velocity, a = Acceleration, t = time, and h = Distance covered
CALCULATION:
Given U1 = U2 = U m/s, V1 = V2 = 0 m/s and a = g (gravitational acceleration downward)
-
At maximum height, the velocity of the object is zero.
- So by the third equation of motion the height gained by any object when it moves freely under gravity,
⇒ V2 = U2 - 2as
⇒ 02 = U2 - 2gh
\(⇒ h =\frac{U^{2}}{2g}\) -----(1)
- So by the first equation of motion the time taken by any object to gain maximum height when it moves freely under gravity,
⇒ V = U - gt
⇒ 0 = U - gt
\(⇒ t =\frac{U}{g}\) -----(2)
- By equation 1 and equation 2 it is clear that the maximum height attains and the time required to attain maximum height when an object moves freely under gravity does not depend on the mass of the body.
- So both the bodies will attain an equal maximum height and take equal time to attain the maximum height.
- Therefore both the statements are correct.
- Hence, option 3 is correct.