A gang of robbers is escaping across city roofs at night. They come to the edge of one building and need to drop down to their getaway car, but aren't entirely sure if they can make the jump or need to head through the building. a) If one of them drops a pebble off the edge of the roof and it hits the ground two seconds later, how fast will they hit the ground if they jump? Give answers in terms of meters per second. b) How high up are they? Give answers in terms of meters. c) Is this a safe jump?

a) They will hit the ground with a speed of 19.6 m/s.

b) They are at a height of 20 m.

c) It is not a safe jump.

Explanation:

Hi there!

a) The equations of height and velocity in function of time of a free falling body are the following:

h = h0 + v0 · t + 1/2 · g · t²

v = v0 + g · t

Where:

h = height of the object at time t.

h0 = initial height.

v0 = initial velocity.

t = time.

g = acceleration due to gravity (-9.8 m/s² considering downward as negative direction).

v = velocity of the object at time t.

Using the equation of velocity, let's find the velocity at which they will hit the ground. The pebble is dropped (initial velocity = 0) and it takes 2 s to reach the ground:

v = v0 + g · t (v0 = 0)

v = g · t

v = - 9.8 m/s² · 2.0 s

v = - 19.6 m/s

They will hit the ground with a speed of 19.6 m/s.

b) Now, we have to use the equation of height:

h = h0 + v0 · t + 1/2 · g · t²

If we place the origin of the frame of reference on the ground, we have to find the initial height (h0) knowing that at t = 2.0 s, h = 0 m

0 m = h0 - 1/2 · 9.8 m/s² · (2.0 s) ²

h0 = 1/2 · 9.8 m/s² · (2.0 s) ²

h0 = 20 m

They are at a height of 20 m.

c) According to a NASA paper (Issues on Human Acceleration Tolerance After Long-Duration Space Flights, figure 10), if you fall with a vertical velocity greater than 17 m/s it is unlikely that you will survive. So, it is not a safe jump.