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

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