Question

When 2 bodies of different masses are thrown vertically upward with equal speed, then consider the following statements:

a) Both the bodies will attain equal maximum height

b) Both the bodies will take equal time to attain maximum height

Which of the above statement is/are correct?

1. Only a is correct
2. Only b is correct
3. Both a and b are correct
4. Neither a nor b is correct.

Answer 1

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.