A man whose mass is 80kg climbs a staircase in 20s and expends power of 120W. Find the height of the staircase.[g = 10ms-2]

Answer Details

To solve this problem, we need to use the formula for power: Power = work done / time taken We also need to use the formula for work done: Work done = force x distance The force here is the weight of the man, which is given by: Force = mass x gravity where g is the acceleration due to gravity. We can rearrange the formula for work done to get the distance: Distance = work done / force Combining these formulas, we get: Power = force x distance / time taken We can rearrange this to get: Distance = Power x time taken / force Substituting the given values: Distance = 120 x 20 / (80 x 10^-2) = 300m Therefore, the height of the staircase is 300m. However, this answer seems unreasonable because it is very high. We need to check if we made an error. We can use another formula to check: Distance = 1/2 x acceleration x time taken^2 where acceleration = gravity. Substituting the values: Distance = 1/2 x 10 x 20^2 = 2000m This is an even higher value, which confirms that we made an error. On closer inspection, we can see that we forgot to convert the mass to weight. Weight = mass x gravity = 80 x 10 = 800N Using this value, we can recalculate the distance: Distance = Power x time taken / force = 120 x 20 / 800 = 3m Therefore, the height of the staircase is 3m. Hence, the correct option is: 3.0m.