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1. Rowan throws a marble from the second floor of his house (initial height : 3m). The speed of the marble as it leaves his hand is always 2.6m/s. Disregard air resistance. In each of the cases below, solve for the speed at which the marble hits the ground. (Make sure to use the conservation of energy in your solution and NOT kinematics) Case A: Thrown straight up. Case B: Thrown straight down. Case C: Thrown out at an angle of 45 above horizontal. Case D: Thrown straight out horizontally.

2. A box of mass 1.5kg is pressed against (but is not attached to) an ideal spring of force constant 37 N/m and negligible mass, compressing the spring a distance 0.6m. After it is released, the box slides up the incline as shown in the figure. (a) If the box stops at a height of 0.26m higher than its initial point, how much energy was lost to friction? (b) If there was no friction, what would the speed of the box be at a height of 0.26m?

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