Question

1. Suppose that you have a mass of 45.7 kg and are standing on frictionless roller skates. Someone then throws you a 2.50 kg mass with a velocity of 14.5 m/s and you catch it. What will be your resultant velocity? (0.75 m/s)

Answer 1

The momentum afterward will be your initial momentum (zero here) plus the momentum of the object 2.5kg*14.5m/s = 36.25kg*m/s.  This will be your final momentum, mv, but now your mass must include the 2.5kg object. so your mass is 45.7+2.5 = 48.2kg.  So mv=36.25 ;  48.2*v=36.25 ; v = 0.752m/s

Answer 2

After catching the ball thrown, the resultant velocity of both mass A and mass B is 0.75m/s.

Given the data in the question;

• Mass A; $m_1 = 45.7kg$

• Initial velocity of mass A; $u_1 = 0$

• Mass B; $m_2 = 2.50kg$

• Initial velocity of mass B; $u_2 = 14.5m/s$

Since mass A caught mass B, meaning the are together, they will both have the same resultant velocity.

Final velocity of both mass A and B; $v =\ ?$

To determine the resultant velocity, we use conservation of linear momentum:

$m_1u_1 + m_2u_2 = ( m_1 + m_2 ) v$

We substitute our given values into the equation

$[45.7kg * 0] + [ 2.50kg * 14.5m/s ] = ( 45.7kg + 2.50kg ) v\\\\2.50kg * 14.5m/s = ( 48.2kg )v\\\\36.25kgm/s = ( 48.2kg )v\\\\v = \frac{36.25kgm/s}{48.2kg} \\\\v = 0.75m/s$

Therefore, after catching the ball thrown, the resultant velocity of both mass A and mass B is 0.75m/s.

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