# Three tasks regarding falling - did I get them right?

• Oct 14th 2012, 05:27 AM
Glyper
Three tasks regarding falling - did I get them right?
1. A rock was thrown at the angle of 30 degrees against the horizontal surface, being given a velocity $\displaystyle V_0=12m/s$. Find the largest height h and the Z - the range of the throw.
2. Two rocks are falling from a roof. The second one begins its fall when the first one has already covered 30cm. Calculate the distance d between these two rocks after 10 seconds counted from the moment the second rock begins its fall.
3. A marble fell from the height h and covered the last 196,2m in 4 seconds. How long was the marble falling? What height was it falling from?

So my thoughts are:

1. $\displaystyle h_{max}=\frac{v_0^2\cdot\sin^2\alpha}{2g}=\frac{14 4*0,25}{2g}=2m$
$\displaystyle Z=\frac{v_0^2\cdot\sin 2\alpha}{g}=\frac{144\sqrt{3}/2}{9,81}=12m$

2. It turns out second rock will go as follows: $\displaystyle s_2=\frac{at^2}{2}={9,81*100}{2}\approx 490,5m$ - where is there an error here? It seems a little weird to me that the rock will cover almost 500 meters. If it does, though, then we have $\displaystyle 0,3=\frac{9,81t^2}{2}$ so $\displaystyle t\approx0,25s$. Then, we know that $\displaystyle v(0,25)=0+9,81*0,25=2,4525m/s$. And finally $\displaystyle s_1=0,3m+2,45*10+\frac{9,81\cdot100}{2}=515,3m$ so they're 24,8 metres apart. Is that OK?

3. How should I approach this? I always end up with two variables ($\displaystyle v_0, s_0$) which I don't know how to calculate.

• Oct 14th 2012, 05:51 AM
HallsofIvy
Re: Three tasks regarding falling - did I get them right?
You seem to be plugging numbers into formulas. Do you know where the formulas come from?
• Oct 14th 2012, 05:58 AM
Glyper
Re: Three tasks regarding falling - did I get them right?
Most of the time I don't. I don't tie my future with physics in any manner but in college I unfortunately have to somehow crawl through it even though it's not really connected to CS which I'm studying. I'm trying to make my best, of course, but I just don't have the time to be really focused on phycisc when there are so many more important - and far more interesting - subjects which I have to pass as well. I'm trying to make some compromise, then.
• Oct 16th 2012, 01:19 PM
Krahl
Re: Three tasks regarding falling - did I get them right?
1. Well I can tell you that your first answer is correct in terms of formulation but I wouldn't round 1.83m to 2m unless you were told to. Also I'm not sure why you rounded 12.7m down to 12m.

2. Correct. I got 24.6m without rounding error along the way. But your answer should still be acceptable.

$\displaystyle S=-\frac{1}{2}gt^2 + v_0 t + S_0 = -196.2$
Here $\displaystyle S_0=0$ since we are simply covering 196.2m "given the starting velocity $\displaystyle v_0$". So you know that t=4s you can solve for $\displaystyle v_0$. Try and see if you can solve it from there.