Superman can leap over tall buildings in a single bound. What does he do to the ground beneath him? Assume his mass is 100.0 ± 0.1 kg and his hips drop by 0.300 ± 0.020 m before he jumps. If he can jump over the top of PNC Plaza (tallest building in Raleigh), which is 164 ± 1 m, calculate the following with uncertainties:
a. Takeoff velocity
b. Acceleration just before takeoff
c. Force on ground at take off

Explanation:

Height reached = 164m

If velocity of launch be u

u² = 2gh

= 2 x 9.8 x 164

= 3214.4

u = 56.7 m /s

difference in u = 1/2  (diff in h / h) x u

1/2 x 1/164 x 56.7

.17 or .2

u = 56.7 ± .2 m /s

or 57± 1

b )  During the displacement of .300 m , there is acceleration to achieve velocity of 56.7 m /s

v² = 2as

a = v² / 2s

= 56.7² / (2 x .3)

= 5358.15 m /s²

diff in a

= 1/2 x (.02 / .3) x 5358.15

178.6

a = 5358.1 ±178.6

c ) force on the ground

mass ( g + a )

= 100 x ( 9.8 +5358.1)

= 536790 N

error  in force = (.1/100 + 178.6 / 5358 ) x 536790

=( .01 +.03)x 536790

= 21471

(536790 ± 21471) N

d.7.5cm is your answer