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.

Could you please help me and check if it's OK?

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?

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.

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.

3. For the last question I'll help you through it.

We are told that the marble covers 196.2m in 4s. So let's write down the distance equation,

$\displaystyle S=-\frac{1}{2}gt^2 + v_0 t + S_0 = -196.2$

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.