A car drives straight off the edge of a cliff that is 50 m high. The police at the scene of the accident note that the point of impact is 140 m from the base of the cliff. How fast was the car traveling when it went over the cliff?
180 m/s
To find the speed of the car when it went off the cliff, we can make use of the laws of motion and the principles of kinematics. Here's the step-by-step explanation of how to solve the problem:
Step 1: Identify the known values:
- Height of the cliff (h) = 50 m
- Distance from the base of the cliff to the point of impact (d) = 140 m
Step 2: Determine the unknown value:
- Speed of the car when it went over the cliff (v)
Step 3: Apply the kinematic equation:
The kinematic equation that relates the initial velocity (v), final velocity (vf), acceleration (a), and displacement (d) is:
vf² = v² + 2ad
Since the car starts from rest, the initial velocity (v) is 0. The final velocity (vf) is the speed of the car when it went over the cliff. The acceleration (a) is due to gravity and is equal to 9.8 m/s², acting downward. The displacement (d) is the height of the cliff, which is 50 m.
Plugging in the known values into the equation:
vf² = 0 + 2 * 9.8 * 50
vf² = 980
Step 4: Solve for vf:
By taking the square root of both sides of the equation, we can find the final velocity (vf):
vf = √(980)
vf ≈ 31.3 m/s
Step 5: Determine the speed of the car:
Since the question asks for the speed, rather than the velocity, we ignore the direction. Therefore, the car was traveling at approximately 31.3 m/s when it went off the cliff.
So, the answer is that the car was traveling at around 31.3 m/s when it went over the cliff.