Answer:
a) v₀ = - 164.62 m / s
, c) y = 122.5 m
Explanation:
We can solve this exercise using the free fall kinematic relations.
We put our reference system on the floor, so the height of the skyscraper is y₀ = 180m and the floor level is y = 0 m
For the boy
y = y₀ + v₀ t - ½ g t²
with free fall its initial speed is zero
y = ½ g t2
For superman
y = y₀ + v₀ (t-5) - ½ g (t-5)²
how superman grabs the lot just before hitting the ground
we look for the time it takes the boy down
t = √ (2 y₀ / g)
t = √ (2 180 / 9,8)
t = 6.06 s
in the equation for superman, we clear the volume and calculate
v₀ (t-5) = -y₀ + ½ g (t-5)²
v₀ (6.06 -5) = -180 + ½ 9.8 (6.06 -5)²
v₀ 1.06 = -174.49
v₀ = - 174.49 / 1.06
v₀ = - 164.62 m / s
the negative sign indicates that the initial speed is down
b) to graph the position of the two we use the table
t (s) Y_boy (m) Y_superman (m)
0 180 180
1 175.1 180
5 57.5 180
6 3.6 10.18
see attachment for the two curves
c) calculate the height that falls a lot in the 5 seconds (t = 5)
y = -1/2 g t²
y = ½ 9.8 5²
y = 122.5 m
for this height superman has not yet left the skyscraper, so the boy hits the ground
