Question

Car A of mass 1500 kg travelling at 25m/s collides with another car B of mass 1000 kg travelling 15m/s in same direction. After collision, the velocity of car A becomes 20m/s. Calculate the velocity of car B after collision ?

Answer 1

This question is all about the conservation of momentum.
Formula for this type of question is.
(m1u1+m2u2=m1v1+m2v2).
m = mass of body.
u = initial velocity.
v = final velocity.
Total momentum of both cars before collision=(1500 x 25 +1000 x 15)
=37500 + 15000
=52500 kg•m/s.
As the conservation of momentum says that total momentum of two bodies which act upon each other remains always equal.
52500=1500 × 20 + 1000 × v
52500=30000 + 1000v
1000v = 52500-30000
v = 22500/1000.
v = 22.5 m/s.
So the velocity of car B will be 22.5 m/s.
PLEASE MARK IT AS A BRAINLIEST ANSWER.

Answer 2

$\large \bold \color {lime}{Given:}$

Mass of car A, m1 = 1500kg

Mass of car B, m2 = 1000kg

and

Velocity of car A before collision, u1 = $\frac25{m}{s}$

Velocity of car B before collision, u2 = $\frac15{m}{s}$

Now,

Velocity of car A after collision, v1 = $20\frac{m}{s}$

$\large \bold \color {lime}{To \: Find:}$

Velocity of car B after collision, v1 = $\frac?{m}{s}$

$\large \bold \color {lime}{Solution:}$

On substituting,

$\implies$ m1u1 + m2u2 = m1v1 + m2v2

$\implies$ $(1500 \: × \: 25) \: × \: (1000 \: × \: 15) \: = \: (1500 \: × \:20) \: + \: (1000 \: × \: v2)$

$\implies$ $37500 \: + \: 15000 \: = \: 3000 \: 1000v2$

$\implies$ $52500 \: - \: 30000 \: = \: 1000v2$

$\implies$ $1000v2 \: = \: 22500$

$\implies$ $v2 \: = \: \large \frac {22500}{1000}$

$\implies$ $v2 \: = \: 22.5\large\frac {m}{s}$

Thus, the velocity of car B (after collision) will be 22.5 $\large\frac {m}{s}$