A boy weighing 100 lb steps on a bathroom scale. He jumps up and lands back on the scale. He lands with an initial speed of 3 m/s and slows down to a stop in a time of 0.2 seconds. During his landing, the bathroom scale reads

To find what the bathroom scale reads during the boy's landing, we need to calculate the force exerted on the scale during his deceleration from landing. 

### Step-by-Step Solution

1. **Determine the Deceleration**: 
   - The boy lands with an initial speed (\(v_0\)) of 3 m/s and comes to a stop in a time (\(t\)) of 0.2 seconds.
   - Using the formula for acceleration (\(a\)) when an object decelerates: 
     \[
     a = \frac{\Delta v}{t} = \frac{0 - 3}{0.2} = \frac{-3}{0.2} = -15 \, \text{m/s}^2
     \]

2. **Calculate the Boy’s Mass**: 
   - Given his weight is 100 lb, we first convert this to mass.
   - The weight in pounds can be converted to mass in kg using \(1 \, \text{lb} = 0.4536 \, \text{kg}\), and the weight in newtons:
     \[
     \text{Mass} = \frac{100 \, \text{lb} \times 0.4536 \, \text{kg}}{9.81 \, \text{m/s}^2} \approx 4.53 \, \text{kg}
     \]

3. **Calculate the Force Due to Deceleration**:
   - The force due to deceleration is given by \(F = ma\).
     \[
     F = 4.53 \, \text{kg} \times 15 \, \text{m/s}^2 = 67.95 \, \text{N}
     \]

4. **Total Force on the Scale**:
   - The total force on the scale during impact includes both the gravitational force (his weight) and the deceleration force.
   - Gravitational force (weight) is:
     \[
     W = mg = 4.53 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 44.44 \, \text{N}
     \]
   - Total force:
     \[
     F_{\text{total}} = W + F = 44.44 \, \text{N} + 67.95 \, \text{N} = 112.39 \, \text{N}
     \]

### Answer

The bathroom scale reads approximately **112.39 N** during the boy's landing.

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Would you like more details, or do you have any questions about the steps?

Here are some related questions to further explore:

1. How would the reading on the scale change if the boy landed with a higher speed?
2. What would happen to the reading on the scale if the deceleration time was shorter?
3. How can we convert the reading in newtons back to pounds for a practical perspective?
4. How does the concept of impulse relate to this problem?
5. What are the effects of air resistance in a real-world scenario where someone jumps on a scale?

**Tip:** Remember that the total force on the scale is the sum of the gravitational force and any additional forces due to acceleration or deceleration.

A boy weighing 100 lb steps on a bathroom scale. He jumps up and lands back on the scale. He lands with an initial speed of 3 m/s and slows down to a stop in a time of 0.2 seconds. During his landing, the bathroom scale reads...

Find out how to calculate the force exerted on a bathroom scale when a boy weighing 100 lb lands with a speed of 3 m/s and comes to a stop in 0.2 seconds. This solution explores deceleration, force due to gravity, and Newton’s laws, suitable for Grades 9-12.

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