1. You are sitting in a sled, at rest on a pond covered with nice, thick, frictionless ice. Your own mass is 86.1$86\mathrm{.}1$ kg,$,$ and the mass of the sled when empty is 12.6$12\mathrm{.}6$ kg.$.$ From shore, someone throws a baseball of mass 0.130$0\mathrm{.}130$ kg to you, and you catch it; the horizontal component of the ball s velocity is 39.1$39\mathrm{.}1$ m/$/$s.$.$ What will be the sled s ($($and your)$)$ speed with respect to the surface of the pond after you catch the ball?

2. This time, your mass is 79.5$79\mathrm{.}5$ kg and the sled s mass is 15.8$15\mathrm{.}8$ kg.$.$ You re on the sled, initially moving to the west at 8.30$8\mathrm{.}30$ cm/$/$s.$.$ From the southern shore, your friend throws a baseball of mass 0.168$0\mathrm{.}168$ kg,$,$ which you catch as it s traveling northward with a horizontal velocity component of 24.3$24\mathrm{.}3$ m/$/$s.$.$ What will be the sled s ($($and your)$)$ speed after catching the ball?

 3. Your mass is 77.0 kg,$,$ and the sled s mass is 13.9 kg.$.$ You start at rest, and then you jump off the sled, after which the empty sled is traveling at a speed of 5.56 m/$/$s.$.$ What will be your speed on the ice after jumping off?