How Do You Calculate the Motion of Freely Falling Objects?

[sap_54]

Hey Everybody,

I am a little perplexed on how to answer this problem, I got an answer, but it doesn't seem to fit within the context of the problem. I don't know if it is because I am using the wrong equation, or if I am just plugging the numbers in wrong:

A rocket is fired vertically upward with an initial velocity of 80.0 m/s. It accelerates upward at 4.00 m/s^2 until it reaches an altitude of 1000 m. At that point, its engines fail and the rocket goes into free flight, with an acceleration of -9.8 m/s^2. (a) How long is the rocket in motion? (b) What is its maximum altitude? (c) What is its velocity just before it collides with the earth?

Also, I was wondering if someone would mind checking this problem for me:

The Height of a helicopter above the ground is given by h=3.00t^3, (h is in m., t is in s.) After 2.00 s, the helicopter releases a small mailbag. How long after its release does the mailbag reach the ground?

3(2)^2=24m.
24m.=0m.+(0m/s)t+1/2(9.8m/s^2)t^2
*t=2.21s.*

Thanks for the help!

 

[Tzar]

i)use v^2=u^2+2as to get the velocity when its at 1000m.
ii)Then use s=ut+1/2*at^2 to get the time of flight. The "u" in the formula is the velocity at the altidue 1000m which you determined in (i). s=-1000 and a=-9.8. find t. this will be the time of flight after it switched off the engines. to get the time b4 it did this use the same forumla only sub in s=1000 a=4 and u=0. add the two times together

iii) for max altidude use same equation as in (i) onlys sub in v=0 a=-9.8 (as opposed to 4) and u= what ever you got in (i) originally. find s and add 100 to it

iv)for final velocity use v=u+at where u is the velocity after the engines are switch off (determine in (i)) a=-9.8 and t is the time off flight after engines are switched off.

 

[quicknote]

I would like to address the first problem regarding freely falling objects. It seems that the initial velocity and acceleration values given do not align with the standard equations for vertical motion. In order to solve this problem accurately, we would need to know the mass of the rocket and any external forces acting on it. Additionally, the question does not specify if the rocket is launched from the ground or from a higher altitude, which would affect the calculations.

Regarding the second problem, it appears that the calculation for the mailbag reaching the ground is correct. However, it is important to note that the equation given for the helicopter's height (h=3.00t^3) assumes constant acceleration, which may not be the case in reality. It would be helpful to have more information about the specific scenario in order to confirm the accuracy of the calculation.

Overall, it is important to always double check the equations and values used in calculations, and to make sure they align with the specific scenario being presented. It may also be helpful to include units in the calculations to ensure accuracy.