A stuntman plans to run across a roof top and then horizontally off it to land on the roof of next bulding. The roof of the next building is 4.9 metre below the first one and 6.2 metre away from it. What should be his minimum roof top speed in m/s. so that he can successfully make the jump?

Options

A. 3.1
B. 4
C. 4.9
D. 6.2

Explanation

To solve the problem of the stuntman jumping from one building to another, we need to determine his minimum rooftop speed. Here’s a step-by-step solution:

### Step 1: Understand the Problem
The stuntman needs to jump horizontally from the first building to land on the second building, which is 4.9 meters below and 6.2 meters away horizontally.

### Step 2: Identify the Variables
- Height of the jump (h) = 4.9 m
- Horizontal distance (x) = 6.2 m
- Acceleration due to gravity (g) = 9.8 m/s²

### Step 3: Calculate the Time of Flight
The time (t) it takes to fall a vertical distance (h) can be calculated using the formula for free fall:
\[ h = \frac{1}{2} g t^2 \]
Rearranging gives:
\[ t^2 = \frac{2h}{g} \]
\[ t = \sqrt{\frac{2h}{g}} \]

### Step 4: Substitute the Values
Substituting the values of h and g into the equation:
\[ t = \sqrt{\frac{2 \times 4.9}{9.8}} \]
\[ t = \sqrt{\frac{9.8}{9.8}} \]
\[ t = \sqrt{1} = 1 \text{ second} \]

### Step 5: Relate Horizontal Distance to Speed
The horizontal distance (x) the stuntman needs to cover can be expressed in terms of his horizontal speed (u) and time (t):
\[ x = u \cdot t \]
Rearranging gives:
\[ u = \frac{x}{t} \]

### Step 6: Substitute the Values
Now substituting the values of x and t:
\[ u = \frac{6.2}{1} = 6.2 \text{ m/s} \]

### Conclusion
The minimum rooftop speed required for the stuntman to successfully make the jump is **6.2 m/s**.

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