Answer:
499.25m
Explanation:
Data obtained from the question include:
m (mass) = 85.5 kg
g (acceleration due to gravity) = 9.8m/s2
h (height) =?
w (work) = 967 (food) Calories
But: 1 food Calorie = 103 calories
Therefore, 967 (food) Calories = 967 x 103 = 99601 calories.
Now we need to covert calories to joules in order to obtain the answer to the question in the right unit of measurement. The conversion from calories to joules is illustrated below:
1 calorie = 4.2J
99601 calories = 99601 x 4.2 = 418324.2J
Work under gravity is given by the formula:
w = mgh
Applying the above formula, we can easily find the height to which the weight-watcher must climb. This is illustrated below:
w = mgh
418324.2 = 85.5 x 9.8 x h
Divide both side by 85.5 x 9.8
h = (418324.2)/(85.5 x 9.8)
h = 499.25m
Therefore, the weight-watcher must climb up to 499.25m if he wishes to work off the equivalent of a large piece of chocolate cake rated at 967 (food) Calories.
The person must climb a height of 499.25m to work off the equivalent of a large piece of chocolate cake rated at 967 (food) Calories.
According to the question we have:
mass of the person, m = 85.5 kg
acceleration due to gravity, g = 9.8m/s2
work done = 967 (food) Calories
we know that:
1 food Calorie = 103 calories
Therefore, in 967 (food) Calories, the total equivalent calories will be = 967 x 103 = 99601 calories.
Now, we convert it to Joules:
1 calorie = 4.2J
So,
99601 calories = 99601 x 4.2 = 418324.2J
Therefore work done required is:
W = 418324.2J
According to the work-energy theorem the work done is given by the change in the potential energy, so
W = mgh
where h is the height climbed by the person
418324.2 = 85.5 x 9.8 x h
h = (418324.2)/(85.5 x 9.8)
h = 499.25m
Learn more about work-energy theorem:
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