A car drives straight off the edge of a cliff that is 54 m high. The police at the scene of the accident observe that the point of impact is 130 m from the base of the cliff. How fast was the car traveling when it went over the cliff?

Options

A. 39 m/s
B. 53 m/s
C. 22 m/s
D. 45 m/s

Answer

To solve the problem of how fast the car was traveling when it went over the cliff, we can break it down into a few steps.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Height of the cliff (h) = 54 m
- Horizontal distance from the base of the cliff to the point of impact (d) = 130 m
- Acceleration due to gravity (g) = 9.8 m/s²

2. **Calculate the Time of Fall:**
The vertical motion can be analyzed using the second equation of motion:
\[ h = \frac{1}{2} g t^2 \]
Rearranging for time (t):
\[ t^2 = \frac{2h}{g} \]
Substituting the values:
\[ t^2 = \frac{2 \times 54}{9.8} \]
\[ t^2 = \frac{108}{9.8} \approx 11.02 \]
Taking the square root:
\[ t \approx \sqrt{11.02} \approx 3.32 \text{ seconds} \]

3. **Calculate the Horizontal Velocity:**
Since there is no horizontal acceleration, the horizontal velocity (u) remains constant. We can find it using the formula:
\[ u = \frac{d}{t} \]
Substituting the known values:
\[ u = \frac{130}{3.32} \approx 39.24 \text{ m/s} \]

4. **Final Result:**
The speed of the car when it went over the cliff is approximately **39.24 m/s**.