Two cliff of heights 120m and 100.4m are separated by a horizontal distance of 16m. If a car has to reach from the first cliff to the second, the horizontal velocity of the car should be

Options

A. `16 ms^(-1)`
B. `4 ms^(-)`
C. `2 ms^(-1)`
D. `8 ms^(-1)`

Answer

To solve the problem of determining the horizontal velocity required for a car to travel from one cliff to another, we can follow these steps:

### Step 1: Determine the height difference between the two cliffs
The heights of the cliffs are given as:
- Height of the first cliff (h1) = 120 m
- Height of the second cliff (h2) = 100.4 m

The height difference (Δh) is calculated as:
\[ \Delta h = h1 - h2 = 120\,m - 100.4\,m = 19.6\,m \]

### Step 2: Calculate the time of flight
The time of flight (t) for an object falling from a height can be calculated using the formula:
\[ t = \sqrt{\frac{2h}{g}} \]
where:
- \( h \) is the height difference (19.6 m)
- \( g \) is the acceleration due to gravity (approximately \( 9.8\,m/s^2 \))

Substituting the values:
\[ t = \sqrt{\frac{2 \times 19.6}{9.8}} = \sqrt{\frac{39.2}{9.8}} = \sqrt{4} = 2\,s \]

### Step 3: Calculate the horizontal velocity
The horizontal velocity (v) can be calculated using the formula:
\[ v = \frac{d}{t} \]
where:
- \( d \) is the horizontal distance (16 m)
- \( t \) is the time of flight (2 s)

Substituting the values:
\[ v = \frac{16\,m}{2\,s} = 8\,m/s \]

### Final Answer
The horizontal velocity of the car should be **8 m/s**.

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