The 1994 Winter Olympics included the aerials competition in skiing. In this event skiers speed down a ramp that slopes sharply
upward at the end. The sharp upward slope launches them into the air, where they perform acrobatic maneuvers. In the women's competition, the end of a typical launch ramp is directed 61° above the horizontal. With this launch angle, a skier attains a height of 16 m above the end of the ramp. What is the skier's launch speed?
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Answer:
Approximately (rounded down,) assuming that
.
The number of repetitions would increase if efficiency increases.
Explanation:
Ensure that all quantities involved are in standard units:
Energy from the cookie (should be in joules, ):
.
Height of the weight (should be in meters, ):
.
Energy required to lift the weight by without acceleration:
.
At an efficiency of , the actual amount of energy required to raise this weight to that height would be:
.
Divide by
to find the number of times this weight could be lifted up within that energy budget:
.
Increasing the efficiency (the denominator) would reduce the amount of energy input required to achieve the same amount of useful work. Thus, the same energy budget would allow this weight to be lifted up for more times.