The circus has come to town, and Lael the Magnificent will kick a grape into her
ID: 1267198 • Letter: T
Question
The circus has come to town, and Lael the Magnificent will kick a grape into her assistant's waiting mouth (not to worry the grape is freshly washed). She starts at the origin and boots the grape at an angle 20.0° east of north. The grape starts from a height of 0.200 meters, with a velocity of 12.0 m/s, 30.0° above the horizontal. Her assistant races to intercept the grape as it descends. Assume that his mouth is 1.75 meters above the ground. (a) How much time elapses after the kick until he catches the grape? (b) At what position must he be standing for the grape to fall into his mouth? Use the x dimension for east-west, and the y dimension for north-south.
Explanation / Answer
a) v= 12 m/s
theta = 30
along y apply newton law of motion
(1.75 - 0.2) = 12*sin30*t - 9.8*t^2/2
4.9t^2-6t + 1.55 = 0
solving
t = 0.82 s
2) positon
after t= 0.82 s
along horizontal distance covered = 0.82*12cos30 = 8.52 m
along east = 8.52sin20 = 2.91 m
along north = 8.52cos20 = 8 m
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