Answer: 1.27 m/s^2
Explanation:
from the question we are given the following
mass of A = 54.5 kg
mass of B = 33.6 kg
mass of A and B = 88.1 kg
velocity of A = 1.51 m/s ( at +x direction )
velocity of B = 2.28 m/s ( at +y direction )
the first diagram below shows the motion of skaters A and B before and after collision
to solve this question we would apply the formula momentum = mass x velocity
momentum of A = 54.5 x 1.51 = 82.3 kgm/s
momentum of B = 33.6 x 2.28 = 76.6 kgm/s
using the momentum obtained above, we rearrange the motion of skaters A and B to form a right angle triangle with the momentum of A on the x axis , momentum of B on the y axis and the unknown momentum of A and B as the hypothenus.
applying Pythagoras theorem momentum of A and B = [tex]\sqrt{(momentum of A^{2} + momentum of B^{2} )}[/tex]
therefore momentum of A and B = [tex]\sqrt{82.3^{2} +76.6^{2} }[/tex]
= 112.4 kgm/s
recall that momentum = mass x velocity
therefore velocity = momentum / mass
velocity of A and B = 112.4 / 88.1 = 1.27 m/s^2
