**Answer:**

a) 323.517 ft/s

b) 402.5 ft

**Explanation:**

At **t = 5s **the student had travelled:

**y = (32/2)*5^2 ft**

**y = 402.5 ft**

The time at which the student will reach the ground is given by:

**900 ft = (32/2 ft/s^2)* t^2**

Solving for t

**t = (1800/32 s^2)^(1/2)**

**t = 7.47667 s**

Therefore Superman need to travell 900 ft in 2.47667 s

The equation of motion of Superman will be:

**ys(t)=v0*t + (32.2/2 ft/s^2)*t^2**

We are looking for a velocity **v0 **such that ys(2.47667 s) = 900 ft:

**900 ft = v0*(2.47667 s) + (32.2/2 * (2.47667)^2) ft**

**v0 = (900 - (32.2/2) (2.47667)^2)/ (2.47667) ft/s**

**v0 = 323.517 ft/s**

The hight of the skyscraper so that even Superman cant save him will be the same as the distance **y0 ** the student has travelled when superman arrived, that is:

**y(t) = - (32.2 (ft/s^2) /2)*(25s^2) = 402.5 ft**