Math Problem Statement

70 kg person climbs up 2 meter in 2.8 seconds. how much per did they gain?

Solution

To determine the power gained, we’ll calculate the work done by the person in climbing 2 meters and then divide it by the time taken.

Step 1: Calculate the Work Done (W)

The work done to lift a mass mm a height hh against gravity is given by: W=mghW = m \cdot g \cdot h where:

  • m=70kgm = 70 \, \text{kg} (mass),
  • g=9.81m/s2g = 9.81 \, \text{m/s}^2 (acceleration due to gravity),
  • h=2mh = 2 \, \text{m} (height).

So: W=70×9.81×2=1373.4JW = 70 \times 9.81 \times 2 = 1373.4 \, \text{J}

Step 2: Calculate the Power (P)

Power PP is the work done per unit time: P=WtP = \frac{W}{t} where t=2.8st = 2.8 \, \text{s}.

Thus: P=1373.42.8490.5WP = \frac{1373.4}{2.8} \approx 490.5 \, \text{W}

Answer

The power gained is approximately 490.5 watts.

Would you like more details or have any questions?


Follow-up Questions:

  1. What would the power be if the height climbed was doubled?
  2. How would the power change if the person took twice as long to climb?
  3. What is the relationship between work, energy, and power?
  4. How does mass affect the power required for the same climb?
  5. Why is gravitational acceleration used in these calculations?

Tip: Power depends on both work done and time taken; reducing time increases power for the same amount of work.

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Math Problem Analysis

Mathematical Concepts

Physics
Work
Power
Energy

Formulas

Work done W = m * g * h
Power P = W / t

Theorems

Work-Energy Principle

Suitable Grade Level

Grades 9-11