A boy of mass 40 kg jumps off a stationary skateboard and moves horizontally with a speed of 1.5 m/s while the skateboard moves in the opposite direction with a speed of 20 m/s. Calculate the mass of the skateboard.
A
60 kg
B
40 kg
C
3 kg
D
2 kg
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Given: mass of boy = 40 kg = m\(_b\), mass of skateboard = ? = m\(_k\), speed of skateboard v\(_x\) = - 20 m/s, speed of boy v\(_y\) = 1.5 m/s
Both the skateboard and the boy were initially at rest.
The total momentum before and after the jump must be equal.
0 = m\(_b\) x v\(_y\) + m\(_k\) x v\(_x\)
0 = 40 x 1.5 + m\(_k\) x (-20)
0 = 60 - 20m\(_k\)
20m\(_k\) = 60
m\(_k\) = \(\frac{60}{20}\) = 3 kg.
Source: WAEC / JAMB / NECO Classroom Archive (Record #72061)