Hey JayDilla, I get 1/3. Here's how:
Kinetic energy due to linear motion is:

where

giving

The rotational part requires the moment of inertia of a solid cylinder

Then the rotational kinetic energy is

Adding the two types of energy and factoring out common terms gives

Here the "1" in the parenthesis is due to linear motion and the "1/2" is due to the rotational part. Since this gives a total of 3/2 altogether, and the rotational part is due to a third of this (1/2), I say it's 1/3.
To determine the height of the object given the time, we simply use the given relation between height and time in the problem statement. It is given as:
h = -16t^2 + 127t
We substitute 55 seconds to t and obtain,
h = -16(55)^2 + 127(55)
h = - 41415
Since we are only looking at the vertical height, we can use the free fall equation to find the height:
h = 0.5*g*t^2, where h is height in m, g is acceleration due to gravity (9.81 m/s^2), and t is time in seconds
h = 0.5*(9.81 m/s^2)*(3.7 s)^2
h = 67.15 m
Therefore, the 7th floor window is 67.15 m above ground level.
Answer:
120 J
Explanation:
KE = mv²/2 = (0.15 kg * [40 m/s]²)/2 = 120 J