Friction force, impulse momentum, mass and speed, direction

Question

1. A sled and rider, gliding over horizontal, frictionless ice at 4.1 m/s, have a combined mass of 70 kg. The sled then slides over a rough spot in the ice, slowing down to 2.6 m/s.
What impulse was delivered to the sled by the friction force from the rough spot?

2. Use the impulse-momentum theorem to find how long (number of sec.) a stone falling straight down takes to increase its speed from 4.5 m/s to 12.5 m/s.

3. Laura, who's mass is 35 kg, jumps horizontally off a 55 kg canoe at 1.5 m/s relative to the canoe. What is the canoe's speed just after she jumps?

4. A spaceship of mass 2.2×106 kg is cruising at a speed of 5.4×106 m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.2×105 kg, is blown straight backward with a speed of 2.5×106 m/s. A second piece, with mass 7.7×105 kg, continues forward at 1.3×106 m/s.

A. What is the speed of the third piece?
B. What is the direction of the third piece? (straight forward or straight backwards)

5. An 8.5 kg dog takes a nap in a canoe and wakes up to find the canoe has drifted out onto the lake but now is stationary. He walks along the length of the canoe at 0.46 m/s, relative to the water, and the canoe simultaneously moves in the opposite direction at 0.17 m/s.
What is the mass of the canoe (in kg)?

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