reinout-g

Thanks Rosala :)

I love all these pictures!

According to your predictions I must be the funniest 

Was hoping to also be the sexiest though

Ai, that sounds awefully unpleasant.

Please don't skin the cat!

Several of our expressions sound very strange when you literally translate them such as;

it is a truth as a cow!

or

I can do this with two finger up my nose

or

That's as correct as a bus

So given 'all craziness on a stick' are there more english expressions that are funny or strange?

Aaah that explains a lot. All right, so we know the profit is the amount the watch sells for minus the amount the watch was bought for. From the initial $500 profit we know that the watch was bought for $2000-$500 = $1500. Given that the watch would now sell for $1800 we know there is a profit left of only $1800-$1500 = $300. The percentage of the profit with respect to the total selling price would be $300/$1800*100 = 16.67%

Reinout 

I'm not sure whether this is an English expression, but in Dutch we have the expression;

'there are several ways that lead to Rome'.

I think that it pretty much sums up these answers.

I didn't know the equation Alan used.

Melody's approach is one I hadn't directly thought of, but I think I like it better than sticking your nose into physics formulas 

I'm lost in the translation of your question. Might be because I don't know the abbreviation wipp...

Could you be more specific please :)

For the last part, we again have

$$v = at$$

where v is the change in velocity.

For the ball going down, the change in velocity is given by.

$$v = 9.8*0.964 \approx 9.45 m/s$$

Since for the ball going upwards a = -9.8 and t = 0.964

the change in velocity for the ball going upwards is given by

$$v \approx -9.45m/s$$

For the ball going downwards, the speed has increased from 13.1 to 22.55m/s

This means that the current kinetic energy is given by

$$E_k = \frac{1}{2}mv^2 = \frac{1}{2}m(22.55)^2$$

Given question a, we knew the ball started with a total energy of

270.045 * m

Therefore the rest of the energy must be left as potential energy, or

$$\begin{array}{lcl}
E_p = 270.045* m - \frac{(22.55)^2}{2}*m = mgh\\
270.045-\frac{22.55^2}{2} = 9.8h\\
h = \frac{270.045-\frac{22.5^2}{2}}{9.8} \approx 1.73 \mbox{ meters}\\
\end{array}$$

For the ball going upwards we know the speed decreased from 13.1 to 13.1-9.45 = 3.65

The kinetic energy at a speed of 3.65m/s is given by

$$E_k = \frac{1}{2}mv^2 = \frac{m3.65^2}{2}$$

This means the rest has become potential energy.

Since we know $$E_t = 270.045$$

$$E_p = E_t-E_k = 270.045*m - \frac{m3.65^2}{2} = m*(9.8)*h$$

Therefore $$h = \frac{270.045-\frac{3.65^2}{2}}{9.8} \approx 26.88 \mbox{ meters}$$

The difference in height is therefore given by

26.88 - 1.73 = 25.15 meters

Reinout 

All right,

so it's way more simpler than I anticipated it to be.

For the first ball we have the formula

$$v = at$$

where v is the change in speed, a is the acceleration and t is the time.

The change in speed for the first ball is 

$$v = v_1-v_0$$

where v0 is the starting speed and v1 is the final speed.

therefore $$v= 23.2-13.1 = 10.1 m/s$$

a is equal to the gravitational force for which we used $$9.8m/s^2$$

Therefore $$t = \frac{v}{a} = \frac{10.1}{9.8} = 1.03\mbox{ seconds}$$

For the second ball there are two parts which we can calculate.

The part where the ball is thrown up and the speed changes from 13.1m/s to 0m/s

and the part where the ball goes down and the speed changes from 0m/s to 23.2 m/s

For the first part we have

$$v = ta$$

We know v = -13.1 and since the gravitational force is working against the speed we have a = -9.8

Therefore $$v = ta \Rightarrow t = \frac{v}{a} = \frac{-13.1}{-9.8} = 1.34 \mbox{ seconds}$$

For the second part we have

$$v = ta$$

v = 23.2m/s, and a = 9.8

Hence $$t = \frac{v}{a} = \frac{23.2}{9.8} = 2.37\mbox{ seconds}$$

Therefore the total time the second ball is in the air is given by

$$t = 1.34+2.37 = 3.71 \mbox{ seconds}$$

Reinout 

Hi there!

You've got a fairly challenging question there, but I can help you out .

Both b***s have potential energy since they are at a balcony at a height of 18.8 meters.

The formula for potential energy is given by

$$E_p = mgh$$

where Ep is the potential energy, m is the mass, g is the acceleration of gravity and h is the height.

Generally g is approximated to be about 9.8 (this differs across the globe).

Therefore $$E_p = m*9.8*18.8 = 184.24*m$$

In addition to that we know that the first ball is thrown downwards with a force of 13.1 m/s

The formula for kinetic energy is given by

$$E_k = \frac{1}{2}mv^2$$

where Ek is the kinetic energy, m is the mass and v is the velocity (speed).

Therefore we know this throw has given an additional energy of.

$$E_k = \frac{1}{2}m(13.1)^2 = 85.805*m$$

So the total energy when the ball is thrown downwards is given by

$$E_t = E_k + E_p = 184.24*m+85.805*m = 270.045*m$$

Now by the first law of thermodynamics we know that energy always remains constant.

If we neglect air resistance, all energy should have been transformed into kinetic energy, a fraction of a milisecond before it hits the ground.

Therefore

$$\begin{array}{lcl}
270.045*m = E_k = \frac{1}{2}mv^2\\
270.045 = \frac{1}{2}v^2 \mbox{ (divide both sides by m)}\\
v^2 = 2*270.045\\
v = \sqrt{2*270.045} \approx 23.2 m/s\\
\end{array}$$

So the answer to the first question is 23.2 m/s

Now for the second ball, let's pretend that the balcony is at height 0. That would mean that when the ball is thrown upwards with a speed of 13.1m/s it will reach a certain height. At this height, all kinetic energy will have transformed into potential energy. 

If we want to calculate this height we can therefore again equate

$$E_k = E_p$$

$$\begin{array}{lcl}
\frac{1}{2}mv^2 = mgh\\
\frac{1}{2}v^2 = gh\\
h = \frac{v^2}{2g}\\
h = \frac{13.1^2}{2*9.8}\\
h \approx 8.76\mbox{meters}
\end{array}$$

Now let's get rid of the assumption that the balcony is at a height of 0.

We now know that the ball loses all it's kinetic energy at a height of 8.76+18.8 = 27.56 meters

This means at this height all it's energy has become potential energy.

We can calculate this potential energy with the equation

$$E_p = m*g*h = m*9.8*27.56 = 270.088*m$$

Again we know that when the ball is just a fraction from the ground all potential energy will have become kinetic energy.

Hence we can again equate this to

$$E_k = \frac{1}{2}mv^2$$

Solving this gives

$$\begin{array}{lcl}
\frac{1}{2}{m}v^2 = 270.088*m\\
\frac{1}{2}v^2 = 270.088\\
v^2 = 2*270.088\\
v = \sqrt{2*270.088}\\
v \approx 23.2m/s\\
\end{array}$$

Since we have neglected air resistance here you can see that the law of thermodynamics apply.

Since both b***s have the same total energy when they leave the balcony, both b***s will have the same total energy when they hit the ground. Since in both cases this energy has totally become kinetic energy. the velocity of both b***s is the same when they hit the ground.

I'll have to look up some formula's with time before I'll be able to answer the other questions (since I haven't done this in a while). 

Reinout 

p.s. I might have made some round-off errors along the way since I've rounded off my answer several times during the calculations. My apologies for that.

Hi there!

Let me help you out here.

There are two formula's you need here.

At the start, the ball only has kinetic energy (speed).

This kinetic energy can be calculated as

$$E_k = \frac{1}{2}mv^2$$

where Ek is the kinetic energy, m is the mass and v is the speed.

At 6.5 meters all the kinetic energy has transformed into potential energy (since we neglect air resistance) which has the following formula;

$$E_p = mgh$$

Where Ep is the potential energy, m is the mass, g is acceleration of gravity and h the height.

Therefore if we equate $$E_p = E_k$$

We have

$$\frac{1}{2}mv^2 = mgh$$

Which we van rewrite to

$$\begin{array}{lcl}
\frac{1}{2}v^2 = gh \mbox{ (divide both sides by m)}\\
v^2 = 2gh\\
v = \sqrt{2gh}\\
\mbox{ fill in g = 9.8 and h = 6.5}\\
v = \sqrt{2*9.8*6.5} \approx 11m/s
\end{array}$$

So the speed at the start was approximately 11 meters per second.

Reinout 

They probably mean writing a number as a product of it's prime factors.

Remember that prime numbers are numbers that can only be divided by itself and 1.

Now every number that is not a prime number can therefore be written as a product of two or more prime numbers. (Since it is the opposite of a prime number). For example 9 = 3*3, 14 = 7*2 and 18 = 3*3*2