Question

A 2 kg ball travelling West at 6 m/s collides with a 3 kg ball travelling South at 4 m/s stick together and move off with a common velocity

i.
Apply appropriate formula to determine the magnitude and
direction of the common velocity Vc​

Answer 1

Momentum of 2 kg ball:

velocity = 6 m/s

momentum (p)= mv

p = (2)(6) kg m/s

p = 12 kg m/s

kg m/s can also be written as 'N'

Force of 2 kg ball = 12 N

Momentum of 3 kg ball:

velocity = 4 m/s

momentum (p) = mv

p = (3)(4)

p = 12 kg m/s

Since kg m/s can also be written as 'N'

Force of 3 kg ball = 12 N

Now that we have the force applied by both the balls, we can find the resultant force using vector addition

2 kg ball's vector = -12 i

3 kg ball's vector = -12 j

Adding both the vectors, we get:

Resultant vector = -12 i -12 j

The speed both the balls will move at, is the magnitude of the resultant vector

Magnitude of the resultant vector:

|R|² = (i vector)² + (j vector)²

|R|² = (-12)² + (-12)²

|R|² = 144 + 144

|R|² = 288

|R| = √288

|R| = 17 m/s (approx)

The balls will move at a velocity of 17 m/s

Direction of the Common velocity:

TanΘ = Opposite / Adjacent

TanΘ = 12 / 12

Tan Θ = 1

Θ = Arctan(1)

Θ = 45 degrees

Therefore, the common velocity will be 45 degrees down from the horizontal