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

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 \( m \) a height \( h \) against gravity is given by:
\[
W = m \cdot g \cdot h
\]
where:
- \( m = 70 \, \text{kg} \) (mass),
- \( g = 9.81 \, \text{m/s}^2 \) (acceleration due to gravity),
- \( h = 2 \, \text{m} \) (height).

So:
\[
W = 70 \times 9.81 \times 2 = 1373.4 \, \text{J} 
\]

### Step 2: Calculate the Power (P)
Power \( P \) is the work done per unit time:
\[
P = \frac{W}{t}
\]
where \( t = 2.8 \, \text{s} \).

Thus:
\[
P = \frac{1373.4}{2.8} \approx 490.5 \, \text{W}
\]

### Answer
The power gained is approximately **490.5 watts**.

Would you like more details or have any questions?

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**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.

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

Learn to calculate the power gained by a 70 kg person climbing 2 meters in 2.8 seconds. This problem uses concepts of work, energy, and power, with detailed calculations and explanations. Suitable for students in Grades 9-11.

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