If a DeLorean rolls gently (vo = 0) off a vertical cliff, how long does it take it to reach a downward velocity of 78 km/h?

V = 78km/h = 78000m/3600s = 21.67 m/s.

d=(V^2-Vo^2)/2g=(469.5-0)/19.6=23.95 m.

t = (V-Vo)/g = (21.67-0)/9.8 = 2.21 s.

NOTE: The 2nd step(d) is not needed.

To calculate the time it takes for a DeLorean to reach a downward velocity of 78 km/h when rolling off a vertical cliff, we can use the laws of motion.

First, let's convert the velocity from 78 km/h to meters per second (m/s), as the standard SI unit for measuring velocity is meters per second.

1 km/h = 1000 m/3600 s
So, 78 km/h = (78 * 1000 m) / 3600 s = 21.67 m/s (approximately)

Now, we can start solving the problem using the equations of motion. In this situation, the DeLorean is only under the influence of acceleration due to gravity, which is approximately 9.8 m/s². We will consider downward motion as positive.

The equation to calculate the final velocity (vf) of an object under constant acceleration is:
vf = vo + at

Where:
vf = final velocity (in m/s)
vo = initial velocity (in m/s)
a = acceleration (in m/s²)
t = time elapsed (in seconds)

In this case, the initial velocity (vo) is zero, as the DeLorean rolls gently off the cliff without any initial downward velocity.

Thus, the equation becomes:
vf = 0 + 9.8t

We need to solve for time (t), so rearrange the equation:
t = vf / 9.8

Now, plug in the given value for vf:
t = 21.67 m/s / 9.8 m/s²

Calculating:
t ≈ 2.21 seconds

Therefore, it takes approximately 2.21 seconds for the DeLorean to reach a downward velocity of 78 km/h when rolling gently off a vertical cliff.