Question

Two cars have a 'rear end' collision. A 1200kg Honda moving at 20m/s strikes a l000kg Ford moving at 15m/s. Their bumpers become locked and they continue to move as one mass. What is their final velocity?

Answer 1

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

Mass of Honda :-

${m_1 = 1200 \: Kg}$

Mass of Ford :-

${m_2 = 1000 \: Kg}$

Velocity of Honda:-

${u_1 = 20 \: m/s}$

Velocity of Ford :-

${u_2 = 15 \: m/s}$

$\huge{\bold{\underline{Explanation:-}}}$

Taking account of Law of conservation of momentum.

$\large{\bold{m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2}}$

As said They move as a same mass.

$\large{ \therefore v_1 = v_2 = v}$

Taking the values.

$\large{\bold{m_1u_1 + m_2u_2 = m_1v + m_2v}}$

Substituting the values,

$\large{ \implies 1200 \times 20 + 1000 \times 15 = v(1200 + 1000)}$

$\large{ \implies 24000 + 15000 = v(2200)}$

$\large{ \implies 39000 = v(2200)}$

$\large{ \implies v = \frac{39000}{2200}}$

$\huge{\boxed{\boxed{v = 17.07 \: m/s}}}$

So,the velocity is 17.07 m/s.

Answer 2

Concept:

According to the conservation of momentum, the sum of the initial momentum of all the objects in the system is equal to the sum of the final momentum of all the objects in the system.

Given:

Mass of the Honda, m₁ = 1200 kg

Velocity of the Honda, v₁ = 20 m/s

Mass of the Ford, m₂ = 1000 kg

Velocity of the Ford, v₂ = 15 m/s

Find:

The final velocity of the cars.

Solution:

According to the momentum conservation,

m₁v₁ + m₂v₂ = m₁u₁ + m₂u₂

The bumpers become locked and both the system are combined, which means the final velocity of the cars becomes the same.

m₁v₁ + m₂v₂ = m₁u + m₂u

m₁v₁ + m₂v₂ = (m₁+ m₂) u

(1200×20) + (1000×15) = (1200+1000)u

u = 39000/2200 = 17.727 m/s

Hence, the final velocity of both cars is the same and equal to 17.727 m/s.

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