Question

car a of mass 1500kg travelling at 25m/s collides with another car b of mass 1000kg travelling at 15m/s in the same direction. after collision, the velocity of car a becomes 20m/s. calculate the velocity of car b after collision​

Answer 1

Explanation:

Given:

• Mass of car A (m1) = 1500 kg
• Mass of car B (m2) = 1000 kg
• Initial velocity of car A (u1) = 25 m/s
• Initial velocity of car B (u2) = 15 m/s
• After collision, final velocity of car A (v1) = 20 m/s

To find:

• Final velocity of car B (v2) after collision = ?

Solution:

Let's recall the conservation of momentum first !

Conservation of momentum says that the momentum before and after collision is always equal.

Since their are two bodies acting upon the situation so,

Mathematically,

Initial momentum of the body becomes m1u1 + m2u2 and

Final momentum becomes m1v1 + m2v2 and hence, they are always equal so the final formula becomes,

==> m1u1 + m2u2 = m1v1 + m2v2

(putting values)...

$= = > \: 1500 \: \times \: 25 \: = \: 1000 \: \times \: v2$

$= = > \: \frac{1500 \: \times \: 25}{1000} = v2$

$= = > \: \frac{15 \: \times \: 25}{10} = \: v2$

$= = > \: \frac{3 \: \times \: 25}{10} = \: v2$

==> v2 = 37.5 m/s

Hence, the velocitiy of car B after collision is 37.5 m/s.

Hope it helped you dear...

Answer 2

$\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}$

Velocity of car B after collision = 25.5 m/s

$\red{\mid{\underline{\overline{\textbf{explanation}}}\mid}}$

Law of conservation of momentum says that momentum of a system of bodies remains conserved if no external force acts on it. Or the Initial momentum of a system of bodies remains same . This law is defined by the expression :

$\bigstar \: m_1 u_1 + m_2 u_2 = m_1v_1 + m_2 v_2 </p><p></p><p></p><p></p><p>$

In this expression :

• m1 = Mass of first body
• u1 = Initial velocity of first body
• m2 = mass of second body
• u2 = Initial velocity of second body
• v1 = Final velocity of first body
• v2 = Final velocity of second body

$\blue{\mid{\underline{\overline{\textbf{Coming to question :-}}}\mid}}$

Important keywords :

• Mass of first car = 1500kg
• Mass of second car = 1000kg
• Initial velocity of first car = 25m/s
• Initial velocity of second car = 15m/s
• Final velocity of first car = 20m/s
• Final velocity of second car = ?

According to law of conservation of momentum, in this case momentum will be conserved, since there is no application of external force. Now after inputting the known values in the expression we get :

$\mapsto \: 1500 \times 25 + 1000 \times 18 = 1500 \times 20 + 1000v_2$

$\mapsto \: 37500 + 18000 = 30000 + 1000v$

$\mapsto \: 55000 - 30000 = 1000v$

$25500 = 1000v$

$\mapsto \: v = \cancel \frac{25500}{1000} = 25.5$

Therefore velocity of Car B after collision is 25.5m/s.

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BY SCIVIBHANSHU

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