Francesco, a pizza chef preparing the dough for your pizza is throwing it to expand it. In this process, you notice that a chunk of it comes off, flying separately from the rest and on to the floor. If Francesco is 6 feet and 3 inches tall, and the chunk flies off vertically straight up from this height at a speed of 1 m/s, with what speed does the chunk hit the ground?

6.12 m/s

Explanation:

In order to solve this we have two parts of this problem, first we have the time that the pizza dough spent going upwards and after that we have a free fall from there, so we will use the free fall formula after we figured out whats the final height the dough reached after being thrown from Francesco's height which is 6ft3inches or 1.90 meters

We first have to find out how much time the dough spent in the air before reaching 0 as final speed and then started the free falling:

The formula would be:

The formula to find out final height would be:

Now we just insert the values we know

So from 1.91 meteres the free fal started we have to just calculate the final velocity with the formula for free fall and velocity:

Since Vo is 0 because we are talking about free falling we just insert the values we know:

So the final speed that the dough hit the ground with is 6.12 m/s

r = 31.8

Explanation:

To start with, we make the following assumptions. Let

r be the radius of semicircular end

l be the length of straight section

a be the area inside track, then

p = 2πr + 2l = 400

a = πr² + 2rl

2πr + 2l = 400

l = 200 - πr, substituting for l in area,

a = πr² + 2r(200 - πr)

a = πr² + 400r - 2πr²

a = 400r - πr²

In order to find our minimum area, we differentiate with respect to r and then it equate to zero

da/dr = 400 - 2πr = 0

r = 200/π, substituting for r in equation for l,

l = 200 - πr

l = 0 m

And since this is not possible, l must be 100 m (the minimum), and

r = (200 - 100)/π

r = 100/π = 31.8 m