Andy (mass 92 kg) and Sam (mass 75 kg) are both on toboggans (each toboggan has a mass of 4.6 kg) travelling on a crash course towards each other. Just as they hit, they lock hands so they move together as one. What is their new speed? In what direction do they travel?
mA = 96.6 kg
vA = 8.8 m/s at 8.7 degrees above horizontal (headed +x direction)
mS = 79.6 kg
vS = 6.7 m/s at 7.3 degrees below horizontal (headed +x direction)
mA + mS = 176.2 kg
vf = ?
mAvA + mSvS = mAvA' + mSvS'
The Attempt at a Solution
Tried finding x and y components and unsure what to do next.. since Andy is headed southeast, do I make that y-component negative? Am I combining too much into these equations? I am so confused with these questions where 2 things are moving at the same time or at non-right angles to each other. Can someone break these problem types down for me so that I have a step by step approach to them? I end up with equations and have no idea how to follow through. Here, I have 2 equations and 2 unknowns in each equation. I don't know what to do next or if this is even correct.
(96.6)(8.8 cos 8.7) + (79.6)(6.7 cos 7.3) = (176.2)(vfcosσ)
7.77 = (vfcosσ)
(96.6)(8.8 sin 8.7) + (79.6)(6.7 sin 7.3) = (176.2)(vfsinσ)
1.11 = (vfsinσ)