Question

​A car drives off a cliff 51 m and lands 196 m away from the base of the cliff. How fast was the object traveling horizontally?

Answer 1

The horizontal speed of the car when it drives off the cliff is approximately 24.9 m/s.

Step-by-step explanation:

The horizontal speed of the car can be calculated using the horizontal motion formula:

`\[ \text{Horizontal distance} = \text{Horizontal speed} * \text{Time} \]`

Since the car is in free fall, the time it takes to reach the ground can be determined using the vertical motion formula:

`\[ \text{Vertical distance} = (1)/(2) * \text{Acceleration due to gravity} * \text{Time}^2 \]`

First, calculate the time of flight using the vertical motion formula:

`\[ 51 \, \text{m} = (1)/(2) * 9.8 \, \text{m/s}^2 * \text{Time}^2 \]`

Solving for time
`(\(t\))`:

`\[ t^2 = (51 * 2)/(9.8) \]`

`\[ t^2 \approx 10.41 \]`

`\[ t \approx 3.22 \, \text{s} \]`

Now, use the time to calculate the horizontal speed:

`\[ 196 \, \text{m} = \text{Horizontal speed} * 3.22 \, \text{s} \]`

`\[ \text{Horizontal speed} \approx (196)/(3.22) \]`

`\[ \text{Horizontal speed} \approx 60.87 \, \text{m/s} \]`

Therefore, the horizontal speed of the car is approximately
`\(60.87 \, \text{m/s}\)`, or rounded to one decimal place, 24.9 m/s.