A 120-kg tackler moving at 5 m/s meets head-on (and tackles) a 80-kg halfback moving at 5 m/s, after which they couple together.
What will be their mutual speed after the collision?
Hint: use conservation of momentum law for INELASTIC collision.
Mass1(tackler) x V1(tackler) + M2(halfback) x V2(halfback) = (M1 + M2) x V(combined)
or
m1(v1) x m2(v2) = (m1+m2)v
=== solve for v ====
(remember, they are running in opposite directions, one velocity should be in the negative direction)
To solve this question, we can use the law of conservation of momentum for an inelastic collision. The law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
In this case, we have a head-on collision between a 120-kg tackler moving at 5 m/s and an 80-kg halfback moving at 5 m/s. After the collision, they couple together, which means they stick together and move as one unit.
Let's calculate the initial momentum before the collision and the final momentum after the collision.
The initial momentum before the collision can be calculated by multiplying the mass of each object by their respective velocities and adding them together:
Initial momentum before collision = (mass of tackler * velocity of tackler) + (mass of halfback * velocity of halfback)
Initial momentum before collision = (120 kg * 5 m/s) + (80 kg * 5 m/s)
= 600 kg⋅m/s + 400 kg⋅m/s
= 1000 kg⋅m/s
Since the tackler and halfback couple together after the collision, their combined mass will be the sum of their individual masses:
Total mass after collision = mass of tackler + mass of halfback
= 120 kg + 80 kg
= 200 kg
Now, we can calculate the final velocity using the formula for the law of conservation of momentum:
Final momentum after collision = Initial momentum before collision
= Total mass after collision * final velocity
Substituting the values:
1000 kg⋅m/s = 200 kg * final velocity
Solving for the final velocity:
final velocity = 1000 kg⋅m/s / 200 kg
= 5 m/s
Therefore, the mutual speed after the collision will be 5 m/s.