Question 307: Centre of Mass and Rotational Motion

Question

There is head-on elastic collision between the two particles moving in the same direction with speeds $5 \mathrm{~m} / \mathrm{s}$ and $3 \mathrm{~m} / \mathrm{s}$ respectively. After collision, the velocity of the first particle becomes $4 \mathrm{~m} / \mathrm{s}$ in the same direction. The velocity of the second particle should be

Accepted Answer

Step 1: List the Information Given
The first particle starts with a speed of $5~\mathrm{m/s}$.
The second particle starts with a speed of $3~\mathrm{m/s}$, in the same direction as the first.
After the collision, the first particle moves at $4~\mathrm{m/s}$, still in the same direction.
The type of collision is elastic, and both particles move along a straight line (head-on).
We need to find the new speed of the second particle ($v_2$) after the collision.
Step 2: Use Elastic Collision Formula for Head-On Collisions
In an elastic head-on collision, the difference in the starting speeds equals the difference in the speeds after the collision, but in the opposite order:
$u_1 - u_2 = v_2 - v_1$
Step 3: Put in the Numbers
Plug in the values we have:
$5~\mathrm{m/s} - 3~\mathrm{m/s} = v_2 - 4~\mathrm{m/s}$
$2~\mathrm{m/s} = v_2 - 4~\mathrm{m/s}$
Step 4: Solve for $v_2$
Add $4~\mathrm{m/s}$ to both sides to find $v_2$:
$v_2 = 2~\mathrm{m/s} + 4~\mathrm{m/s}$
$v_2 = 6~\mathrm{m/s}$
Step 5: Check the Direction
Because the answer is positive, this means the second particle moves in the same direction as before, just faster.
Step 6: Final Answer
The second particle's speed after the collision is $6~\mathrm{m/s}$, in the same direction as before.
The matching answer choice is:
Option A: $6~\mathrm{m/s}$ in the same direction.
So, the correct answer is $\boxed{6~\mathrm{m/s}~	ext{in the same direction.}}$

Answer

$6 \mathrm{~m} / \mathrm{s}$ in the same direction.

Answer

$4 \mathrm{~m} / \mathrm{s}$ in the same direction.

Answer

$2 \mathrm{~m} / \mathrm{s}$ in the opposite direction.

Answer

$3 \mathrm{~m} / \mathrm{s}$ in the same direction.

Centre of Mass and Rotational Motion

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