Question

A body of mass 2 kg is dropped from a height of 20 m. It accelerates uniformly at the rate of 10 m/s2until it hits the ground. Calculate the initial momentum and the momentum just before it strikes the ground.​

Answer 1

Given :

➳ Mass of body = 2kg

➳ Initial velocity = zero (freefall)

➳ Acc. due to gravity = 10m/s²

To Find :

➔ Initial momentum.

➔ Final momentum just before it strikes the ground.

SoluTion :

⇒ Momentum is defined adms the product of mass and velocity.

⇒ It is a vector quantity having both magnitude as well as direction.

⇒ SI unit : kg m/s or N s

⇒ For a body falling freely under the action of gravity, g is taken positive.

✴ Final velocity at which body hits the ground :

➠ v² - u² = 2gH

➠ v² - (0)² = 2(10)(20)

➠ v² = 400

➠ v = √400

➠ v = 20 m/s

✴ Initial momentum :

➛ Pi = m × u

➛ Pi = 2 × 0

➛ Pi = 0 Ns

✴ Final momentum :

⟶ Pf = m × v

⟶ Pf = 2 × 20

⟶ Pf = 40 Ns

Answer 2

Answer:

Mass - 2 kg

Height = 20 m

Gravity - 10 m/s²

Initial Momentum :

Since the Ball is in rest, the initial velocity of the ball will be 0 m / s. Hence we know that,

Initial Momentum = Mass * Initial Velocity ( u ) 

=> Initial Momentum = 2 kg * 0 m / s = 0 kg . m / s

Final Velocity ( v ) = √ ( 2gh )

Final Velocity = √ ( 2 * 10 * 20 )

Final Velocity = √ 400 => 20  m / s

Hence Final Momentum = Mass * Final Velocity ( v )

=> Final Momentum = 2 * 20

=> Final Momentum = 40 kg . m / s

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