Question

Two stones are thrown vertically upwards simantaneously with their velocities u²1and u²2 respectively. Prove that the heights reached by them would be in the ratio of u²1:u²2. (Assume upward acceleration is -g and downward acceleration to be +g.)

Answer 1

so here is the answer

Answer 2

Given:-

• Initial velocity of stone A = u₁
• Initial velocity of stone B = u₂
• To assume upward acceleration (+ g) and downward acceleration (- g).

To Prove: Heights reached by the stones are in ratio u₁² : u₂².

...

Let the height attained by stone A be = h₁

And height attained by stone B be = h₂

Since they are thrown vertically upwards, a time will come when they will become stationary objects. Or have 0 m/s as their final velocity.

We know,

2gh = v² - u²

where,

• g = Acceleration due to gravity,
• h = Height,
• v, u = Final and initial velocities respectively.

Stone A’s height:-

2gh = v² - u²

→ - 2gh₁ = - u₁²

[Acceleration = - g (Upward); v = 0.]

→ h₁ = u₁²/2g

Stone B’s height:-

2gh = v² - u²

→ - 2gh₂ = - u₂²

[Acceleration = - g (Upward); v = 0.]

→ h₂ = u₂²/2g

NOW, ratio between the heights:-

h₁ : h₂

= h₁ / h₂

= (u₁²/2g)/(u₂²/2g)

= (u₁²/2g)/(u₂²) × 2g

= u₁²/u₂²

= u₁² : u₂²

Hence, Proved.