Question

A dog of mass 10 kg sits on a skateboard of mass 2 kg that is initially traveling south at 2 m/s. The dog jumps off with a velocity of 1 m/s north rela-tive to the ground. Which of the following is the best estimate of the velocity of the skateboard immediately after the dog has jumped?

(A) 1 m/s north(B) 1 m/s south(C) 3 m/s south (D) 7 m/s south(E) 17 m/s south

Answer 1

Answer:

17 m/s south

Explanation:

$m_1$ = Mass of dog = 10 kg

$m_2$ = Mass of skateboard = 2 kg

v = Combined velocity = 2 m/s

$u_1$ = Velocity of dog = 1 m/s

$u_2$ = Velocity of skateboard

In this system the linear momentum is conserved

$(m_1+m_2)v+m_1u_1+m_2u_2=0\\\Rightarrow u_2=-\dfrac{(m_1+m_2)v+m_1u_1}{m_2}\\\Rightarrow u_2=-\dfrac{(10+2)2+10\times 1}{2}\\\Rightarrow u_2=-17\ m/s$

The velocity of the skateboard will be 17 m/s south as the north is taken as positive