Question

A 0.3 kg hockey puck is sliding along the ice at 17 m/s due East when it hits a 1.4kg water bottle covered in gum sitting at rest. The puck and water bottle stick together and end up going 40.0 degrees South of East after the collision. What is the resultant velocity of the stuck puck?

Answer 1

`3.91m\/s`

Step-by-step explanation

Parameters given:

Mass of hockey puck, m1 = 0.3 kg

Mass of bottle, m2 = 1.4 kg

Initial velocity of hockey puck, u1 = 17 m/s (taking East as positive direction)

Initial velocity of bottle, u2 = 0 m/s

Final direction of bottle/puck = 40° South of East

To find the resultant velocity of the puck, we have to apply the principle of conservation of momentum, which states that:

This implies that the final momentum must be equal to the initial momentum.

Therefore:

`m_1u_1+m_2u_2=(m_1+m_2)v\cos \theta`

where v represents the final velocity of the puck/bottle and cosθ indicates that the direction of the final velocity is at an angle θ.

Solve for v by substituting the given values:

`\begin{gathered} (0.3\cdot17)+(1.4\cdot0)=(0.3+1.4)\cdot v\cdot\cos 40 \\ \Rightarrow5.1=1.302\cdot v \\ \Rightarrow v=(5.1)/(1.302) \\ v=3.91m\/s \end{gathered}`

That is the final velocity of the stuck puck.