A healthy young man standing at a distance of 7 m from 11.8 m high building sees a kid slipping from the top floor. With what speed (assumed uniform) should he run to catch the kid at the arms height (1.8m)?

Explanation

To solve the problem, we need to determine the speed at which the young man should run to catch the kid who is slipping from the top of the building. Here’s a step-by-step solution:

### Step 1: Understand the scenario
The building is 11.8 meters high, and the young man is standing 7 meters away from the base of the building. The kid slips from the top of the building and needs to be caught at a height of 1.8 meters.

### Step 2: Calculate the distance the kid falls
The kid falls from a height of 11.8 meters to 1.8 meters. The distance the kid falls (s) is:
\[ s = 11.8 \, \text{m} - 1.8 \, \text{m} = 10 \, \text{m} \]

### Step 3: Use the equations of motion
The kid is falling under the influence of gravity, so we can use the second equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
where:
- \( s \) = distance fallen = 10 m
- \( u \) = initial velocity = 0 (the kid starts from rest)
- \( a \) = acceleration due to gravity = 9.8 m/s²
- \( t \) = time taken to fall

Substituting the values into the equation:
\[ 10 = 0 \cdot t + \frac{1}{2} \cdot 9.8 \cdot t^2 \]
This simplifies to:
\[ 10 = 4.9 t^2 \]

### Step 4: Solve for time (t)
Rearranging the equation gives:
\[ t^2 = \frac{10}{4.9} \]
Taking the square root:
\[ t = \sqrt{\frac{10}{4.9}} \]
Calculating this gives:
\[ t \approx \sqrt{2.04} \approx 1.43 \, \text{s} \]

### Step 5: Calculate the speed of the young man
The young man needs to cover a horizontal distance of 7 meters in the same time it takes for the kid to fall. The speed (U) of the young man can be calculated using:
\[ U = \frac{\text{distance}}{\text{time}} = \frac{7 \, \text{m}}{t} \]
Substituting the value of \( t \):
\[ U = \frac{7}{1.43} \approx 4.90 \, \text{m/s} \]

### Final Answer
The speed at which the young man should run to catch the kid is approximately **4.90 m/s**.

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