Jonathan and Jane are sitting in a sleigh that is at rest on frictionless ice. Jonathan’s weight is 800 N, Jane’s weight is 600 N, and that of the sleigh is 1000 N. They see a poisonous spider on the floor of the sleigh and immediately jump off. Jonathan jumps to the left with a velocity of 5.00 m/s at 30.0o above the horizontal (relative to the ice), and Jane jumps to the right at 7.00 m/s at 36.9o above the horizontal (relative to the ice). Calculate the sleigh’s horizontal velocity (magnitude and direction) after they jump out.
Solution 104P Step 1: Weight of Jonathan w = 800 N 1 Weight of Jane w = 600 2 Weight of the Sleigh w = 1000N3 Final velocity of Jonathan v = -5.00 m/s (-x direction) 1 Angle above horizontal by Jonathan = 30.0° Final velocity of Jane v = 7.002/s (+x direction) Angle above horizontal by Jane = 36.9° Step 2: To find the final velocity (v ) of t3 sleigh after they jump out The two guys sit on the sleigh initially. And the sleigh also in the rest position. Total initial momentum is zero as all of them are at rest. Step 3: Final velocity may be calculated by assuming the situation as collision, after collision the total momentum is conserved. The law of conservation of momentum states that, the total momentum before collision is equal to the total momentum after collision. Mathematically 0 = P 1P + 2 3 Where P , P & P final momenta. 1 2 3 0 = m v + m v + m v -----(1) 1 1 2 2 3 3