Answer:
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.
is the mass
is the gravitational acceleration which is equal to g = 9.8 m/s²
is the height