# Will take non zero values increasing the kinetic

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will take non-zero values, increasing the kinetic energy. The correct answer is therefore A . 2. Three balls are thrown from a platform 20 m high with the same initial speed. Ball A is thrown vertically up. Ball B is thrown horizontally. Ball C is thrown at an angle of 30 above the horizontal. Rank the balls by their speed at impact with the ground, highest to lowest. by (a) A=B=C. 4 (b) A C B. (c) B C A. (d) B=A C. (e) B A C. All of the objects are thrown with the same speed, from the same height, and thus have equal total energy E 1 2 mv 2 mgh . When colliding with the ground this energy is conserved, converting to a kinetic energy equal among the masses. Given the equal kinetic energies all the balls have equal speeds. Choice A . 2

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3. A block of mass m is moving on a smooth (frictionless) horizontal table on which there are two springs attached at each end, separated by some distance on which the block can move freely. On the left is a spring with spring constant k , while the spring constant of the spring on the right is 2 k , as shown in the following figure: 2 m k 2 k Initially the block moves towards the left, hits the left spring which it compresses by a distance d . The block then rebounds as the spring extends, moves freely to the right and eventually hits the right spring which it now compresses. The distance by which the spring on the right is compressed is (a) d 2. 4 (b) d 2. (c) 2 d . (d) 2 d . (e) 2 1 2 d . The block stops after compressing the left spring a distance d , thus having potential energy 1 2 kd 2 . After it stops on the right spring, compressing it a distance x . By conservation of energy: 1 2 kd 2 1 2 2 k x 2 x d 2 . Choice A . 3

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