A 85.5 kg weight-watcher wishes to climb a mountain to work off the equivalent of a large piece of chocolate cake rated at 967 (food) Calories. How high must the person climb? The acceleration due to gravity is 9.8 m/s 2 and 1 food Calorie is 103 calories

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.