University of Melbourne

ABPL 90324

Question 1 Eggsy and Lancelot’s cousin, Spearalittle, modified an old Kingsman cigar-lighter cannon to launch ice cubes. The ice cubes are launched vertically upward so that they splash at just the right speed into a Kingsman glass that Eggsy designed for his new Gin Martini recipe, as shown. Eggsy encoded the launch speed (to stop Harry from stealing his recipe) with the simple restriction that, after launch, the ice cubes must travel 1% of their vertical distance during the last second of their upward travel. What is the muzzle speed, v, of the ice cube? Answer in m s . A)147 B)49 C)196 D)245 E)98 Solution Let h be the height at which the cube travels. We know that the last 1% of it’s height up is done in 1 second. ∆d = 1 2 a∆t 2 0.01h = 1 2 × 9.81 m s 2 × (1s) 2 h = 1 2 × 9.81 m s 2 × (1s) 2 0.01 = 490.5m We can just use conservation of energy to find the velocity of the ice cube when it was shot up. 1 2 mv2 = mgh v = p 2gh = r 2(9.81 m s 2 )(490.5m) = 98.1 m s 2 Thus the speed of the cube when shot is 98.1 m s 2 and thus the answer is E