Question

a boy of mass 40 kg moving with velocity 5m/s jumps into a skating board of mass 3 kg at rest if the boy and skating board move together what is the velocity?
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Answer 1

Answer

• Velocity of skating board and boy moving together = 4.65 m/s

Explanation

Given:-

A boy of mass 40 kg moving with 5 m/s jumps on a skateboard of mass 3 kg at rest. On jumping the skateboard along with boy starts moving.

• Mass of boy, m = 40 kg
• Initial velocity of boy, u = 5 m/s
• Mass of skateboard, M = 3 kg
• Initial velocity of skateboard, U = 0 m/s

To find:-

• Final velocity of combined system of boy and skateboard, v =?

Knowledge required:-

Law of conservation of linear momentum

• The law of conservation of linear momentum states that the momentum of an isolated system remains constant. [i.e., Total momentum before collision = total momentum after collision.]

For two bodies of masses m and M, with initial velocities u and U and final velocities after collision  v and V.,

        m u + M U = m v + M V

Solution:-

Using the law of conservation of momentum

→ m u + M U = m v + M v

→ m u + M U = v ( m + M )

→ 40 × 5 + 3 × 0 = v × ( 40 + 3 )

→ 200 = v × 43

→ v = 200/43 m/s

→ v = 4.65 m/s  [approx.]

Therefore,

• Final Velocity of combined system of skateboard and boy will be 4.65 m/s.

Answer 2

Question

a boy of mass 40 kg moving with velocity 5m/s jumps into a skating board of mass 3 kg at rest if the boy and skating board move together what is the velocity?

solve time :-

We have ,

Mass of the boy , M= 40 kg

Velocity of boy , u = 5 m/s

Mass of skating board , m = 3 kg

Velocity of skating board , v = 0 [ at rest ]

Let the Velocity of cart [ boy and sakting together ] be V .

As no external force acts on the system

So According to the law of conservation of Momentum .

Intital momentum = Final momentum

$\sf\implies\:Mu+mv=(m+M)V=>Mu+mv=(m+M)V$

$\sf\implies\:40\times5+3\times0=(40+3)V=>40×5+3×0=(40+3)V$

$\sf\implies\:43V=200=>43V=200$

$\sf\implies\:V=\dfrac{200}{43}⟹V=$

$\rm\implies\:V=4.65ms^{-1}=>V=4.65ms$

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Given,

More About the topic :-

• Conservation of Momentum :

If no external force acts on the system of constant mass the total momentum of the system remains constant

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