Two physics questions: Acceleration?

Question

I was assigned a sheet full of problems in physics class, and I got them all except these two. Could anyone help me please?

1. A car is stopped at a stoplight. As soon as it turns green, it accelerates 10 ft./s^2 while a truck that didn't stop, having a constant velocity of 30 ft./sec passes the car.

How far beyond the starting point will the car overtake the truck, and how fast will the car be traveling at this time?

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2. A student wants to test acceleration due to gravity, so he climbs to the top of a 900 ft. tall building and falls off the roof. 5 seconds later, Superman arrives at the scene and flies down to the bottom to catch him (Assume Superman's acceleration to be acceleration due to gravity).

A. What must Superman's Initial velocity be to catch the student immediately before the student would hit the ground?

B. What must be the height of the building so that even Superman cannot save him?

Answer 1

** Q1 **
truck's displacement = car's displacement
vt = 0.5at²
==> t = 2v/a = 2(30 ft/s)/(10 ft/s²) = 6 seconds later the car overtakes the truck

How far?
d = vt = (30 ft/s)(6 s) = 180 ft

How fast is the car traveling?
v = 0.5at² = 0.5(10 ft/s²)(6 s)² = 180 ft/s


*** Q2 ***
student falls h = 900 ft in t seconds, superman must last (t-5) seconds to cover h = 900 ft

h = 0.5gt² (student)
h = v0*(t-5) + 0.5g*(t-5)² (superman)

t = sqrt(2h/g)

then

h = v0*[sqrt(2h/g) - 5] + 0.5g*[sqrt(2h/g) - 5]²

v0 = {h - 0.5g*[sqrt(2h/g) - 5]²} / [sqrt(2h/g) - 5]
v0 = (800 ft)/(2.5 s) = 320 ft/s


there is no time enough if [sqrt(2h/g) - 5] < 0
==> h < 12.5g ==> h < 400 ft
superman arrives too late and he's not able to save the boy

Answer 2

1.
vt = at²/2
t = at²/2v
1/t = a/2v
t = 2v/a = 60/10 = 6 sec

2.
Falling boy:
x = at²/2
t = sqrt(2x/a)
..= sqrt(1800/32)
..= 7.5 sec

Superman (t = 7.5 - 5 = 2.5 sec):
x = vt + at²/2
v = (x - at²/2)/t
..= (900 - 32*2.5²/2)/2.5
..= 320 ft/sec

I'm not sure what is implied by Part B. We have no idea what the limit is to Superman's initial speed (aside from relativistic limits).