 #1
arhzz
 240
 46
 Homework Statement:

The equation of motion applies
A rocket starts at a speed of 42 m / s.
(a) How far did she fly after 1 s?
(b) What is the maximum height? When does the rocket reach its maximum altitude? ¨
(c) At what speed and when does the rocket hit the earth again?
(d) What initial speed would have been necessary for the rocket to take 20 s ¨
hits back on earth?
(e) Show that the rocket for the upward movement and for the downward movement ¨
takes the same length regardless of the initial speed.
 Relevant Equations:
 s(t) = s0 + v0t  g/t^2
Hello! I've done the following to solve this problem.
a) Here I simply put in the time in the equation, s0 is = 0 and after that it was pretty much done
$$s(t) = 42 *1  \frac {9,81*1^2} {2} = 37,09m $$
b) Now here to see when the rocket reaches it maximum altitude and what height it is, first we need to check at what point did the rocket reach its maximum altitude. Since it was at its peak it wasnt moving anymore so we can assume that s(t) and s0(t) = 0 and if we input that into the equation and try to get t out.
$$ 0 = 42 * \frac {9,81*t^2} {2} $$ Now we multiply by 2 get t to the left and t should be $$ t= 4,28 s$$
c) Now here for the velocity I simply assumed that it is also 42 m/s, actually 42 m/s. Because after it reaches it highest point its speed is 0. It will than have to travel the same distance to reach the ground. So the time and speed should be the same, simply in the other direction. That said the entire time the rocket was in the air should be $$ t_{total} = t1+t2 = 8,56 s $$
d) Now here is where I'm not getting a few things. So the time is 20 so t= 20. Now to get the v0 I simply rearange the equation of motion.
$$ s(t) = v0t  \frac{gt^2}{2} $$ Multiply by 2
$$ 2s = 2v0t  g *t^2$$ Now the 2 on the right an the left should cancel out so
$$ s = vot  g* t^2 $$ Now since we want v0 we move it to the left and we move s to the right side of the equation
$$ v0 = \frac {g*t^2} {t*s} $$
Now when I plug in all the values I get v0 = 5,28 m/s and that is obviously wrong. Now we are given the correct solution it is 98,1 m/s but I cannot get it. The steps that they took to get the solution are as following;
$$2s = v0t  gt^2 $$
$$ v0 = \frac {gt} {2} $$
Now I have no idea how u get from the first equation to this. If anyone understands this I'd be grateful if he could give me a litle bit of insight.
Thanks!
a) Here I simply put in the time in the equation, s0 is = 0 and after that it was pretty much done
$$s(t) = 42 *1  \frac {9,81*1^2} {2} = 37,09m $$
b) Now here to see when the rocket reaches it maximum altitude and what height it is, first we need to check at what point did the rocket reach its maximum altitude. Since it was at its peak it wasnt moving anymore so we can assume that s(t) and s0(t) = 0 and if we input that into the equation and try to get t out.
$$ 0 = 42 * \frac {9,81*t^2} {2} $$ Now we multiply by 2 get t to the left and t should be $$ t= 4,28 s$$
c) Now here for the velocity I simply assumed that it is also 42 m/s, actually 42 m/s. Because after it reaches it highest point its speed is 0. It will than have to travel the same distance to reach the ground. So the time and speed should be the same, simply in the other direction. That said the entire time the rocket was in the air should be $$ t_{total} = t1+t2 = 8,56 s $$
d) Now here is where I'm not getting a few things. So the time is 20 so t= 20. Now to get the v0 I simply rearange the equation of motion.
$$ s(t) = v0t  \frac{gt^2}{2} $$ Multiply by 2
$$ 2s = 2v0t  g *t^2$$ Now the 2 on the right an the left should cancel out so
$$ s = vot  g* t^2 $$ Now since we want v0 we move it to the left and we move s to the right side of the equation
$$ v0 = \frac {g*t^2} {t*s} $$
Now when I plug in all the values I get v0 = 5,28 m/s and that is obviously wrong. Now we are given the correct solution it is 98,1 m/s but I cannot get it. The steps that they took to get the solution are as following;
$$2s = v0t  gt^2 $$
$$ v0 = \frac {gt} {2} $$
Now I have no idea how u get from the first equation to this. If anyone understands this I'd be grateful if he could give me a litle bit of insight.
Thanks!