A 1.40 kg snowball is fired from a cliff 11.9 m high. The snowball\'s initial ve

Question

A 1.40 kg snowball is fired from a cliff 11.9 m high. The snowball's initial velocity is 12.5 m/s, directed 29.0° above the horizontal. (a) How much work is done on the snowball by the gravitational force during its flight to the flat ground below the cliff?(b) What is the change in the gravitational potential energy of the snowball-Earth system during the flight? (c) If that gravitational potential energy is taken to be zero at the height of the cliff, what is its value when the snowball reaches the ground?

Explanation / Answer

Initial Velocity = 12.5 m/s at 29° above horizontal
Initial Vertical Velocity Component = 12.5*sin 29 = 6.060 m/s
Initial Horizontal Velocity Component = 12.5*cos 29 = 10.93 m/s

g = 9.81 m/s²
t = time to reach max height = 6.060/9.81 = 0.6177 s
max height above cliff = h = 1/2gt² = (0.5)(9.81)(0.6177)² = 1.87 m
Total Vertical distance of snowball = 11.9 + 1.87 = 13.77 m
Mass of snowball = 1.4 kg
Weight of snowball = 1.4(9.81) = 13.73 N
Work done by weight of snowball = 13.73*(13.77) = 189 J

b) Change in gravitational potential energy of snowball-Earth system = 189 J

C) If ref level is at cliff the change in gravitational potential energy = -11.9* (13.73) = -163.38 J

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