Problem 20.

The car drives straight off the edge of a cliff that is 57 m high. The investigator at the scene of the accident notes 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?

Solution:

Motion along axis x (horizontal axis) is the motion with constant velocity. So we can write down the dependence of x-coordinate as a function of time:

Where is the initial velocity (the initial velocity has only x-component, its direction is along axis x).

We know the final x-coordinate of the car – it is 130 m. But we do not know the traveled time and the initial velocity.

We can find the traveled time from the motion along axis y. This is the motion with constant acceleration (free fall acceleration). We know the height of the cliff – this is the traveled distance in y-direction. We know that initial velocity (in y-direction) is 0. Then we can write the following equation:

From this equation we can find the traveled time:

Then from the motion along axis x we have:

From this equation we can find initial velocity: