kinematics

• Jiemanutz

  6 Mar 09, 18:42

  The hot air balloon is now travelling vertically upward at a constant speed of 5 m/s. When it is 30m above the ground,a second package is released from the balloon.

  How long does the second package take to reach the ground?

  What is the speed of the package just b4 it hits the ground?

   

  thanks

• iamapebble

  6 Mar 09, 19:22

  Taking upwards and right as positive, and since any object dropped from a moving object will have a initial velocity equals to the moving object,

  We have:
  s = ut + 1/2at^2
  -30 = 5t + 1/2(-9.81)t^2
                 .
                 .
                 .
  t = 3.03s or t = -2.01s (rejected because time cannot be negative)

  Next, speed just before the package hits the ground is actually the final velocity of the package, therefore we have:

  a = (v-u)/t
  -9.81 = (v - 5)/3.03s
  v = -24.7ms^-1 (velocity is negative due as it is moving downwards)
  
  However, since question requires speed, we can just leave as:

  Speed of package just before it hits the ground = 24.7ms^-1.

• Darkness_hacker99

  6 Mar 09, 19:25

  Speed of the package just before hit the ground (assume negligible air resistence):

  Let v be the velocity, h be the height, g be gravitation constant

  v = sqrt 2gh.

   

  G acceleration. 9.8m/s (assuming). Meaning every second, it's adds 9.8m to the distant it dropped. ie. 9.8, 19.6, etc.

  Time taken for the second object to fall down = 30/9.8m/s = 3.06 seconds.

   

   

  P.S I long time didn't do physics le. dunno whether correct. Those who know, please correct me alright >.<" Thanks~

   

   

   

   

• Jiemanutz

  6 Mar 09, 20:22

  the answers are 3.03s and 24.m/s respectively

   

  thanks all

• Darkness_hacker99

  6 Mar 09, 22:09

  I learned something new today. :)

• eagle

  7 Mar 09, 09:26

  well done iamapebble

   

• blueftw

  8 Mar 09, 20:04

  how does the mass of a projectile affect it's range??

• eagle

  8 Mar 09, 21:07

  Originally posted by blueftw:

  how does the mass of a projectile affect it's range??

  it doesn't

  the initial velocity affects it

• 16/f/lonely

  8 Mar 09, 22:40

  Originally posted by eagle:

  it doesn't

  the initial velocity affects it

  
  it doesn't provided air resistence is ignored.

• eagle

  8 Mar 09, 23:06

  Originally posted by 16/f/lonely:

  
  it doesn't provided air resistence is ignored.

  yup

  i forgot about air resistance, or rather, fluid resistance

• Jiemanutz

  9 Mar 09, 22:06

  how do we know when to write the correct sign convention for displacement and acceleration? wad is the use of a reference point?

   

  thanks

• 16/f/lonely

  9 Mar 09, 22:07

  Originally posted by Jiemanutz:

  how do we know when to write the correct sign convention for displacement and acceleration? wad is the use of a reference point?

   

  thanks

  
  There's no correct/wrong direction.

  That's why there's a reference point.

  Your answer can be negative/positive.

• blueftw

  9 Mar 09, 23:19

  so in conlclusion you all are saying that when there is air resistance, the mass of the projectile affects the range?

• crimson soldier

  9 Mar 09, 23:24

  Originally posted by blueftw:

  so in conlclusion you all are saying that when there is air resistance, the mass of the projectile affects the range?

  when there is air resistance, ma= mg-bv^2, solve the second order differential equation to obtain x as a function of t, and then differentiate it once again to get v!

   

  ....no wait this is O levels so leave out air resistance please : D

• 16/f/lonely

  10 Mar 09, 20:57

  Originally posted by blueftw:

  so in conlclusion you all are saying that when there is air resistance, the mass of the projectile affects the range?

  
  Logically speaking.

  Of course!

  If you throw a ping pong ball and a fish ball, chances are the fish ball goes further.

  Because the air particles have to do more work on the thing you throw if its heavier to slow it down the same amount as the lighter object because of momentum. F= ma, Momentum = mV.

  The presence of air resistence complicates things further. You have to take surface area into consideration as well. It does not just stop at the area that is facing the direction you threw the object. Because of friction between the air particles and the object, obviously, the larger the surface area, the more friction and hence resistence. Not to mention, the less laminar the flow of the air around the object, the higher the resistence due to turbulence.

  Ok, I shall stop here.

   

• eagle

  10 Mar 09, 22:42

  Originally posted by 16/f/lonely:

  
  Logically speaking.

  Of course!

  If you throw a ping pong ball and a fish ball, chances are the fish ball goes further.

  Because the air particles have to do more work on the thing you throw if its heavier to slow it down the same amount as the lighter object because of momentum. F= ma, Momentum = mV.

  The presence of air resistence complicates things further. You have to take surface area into consideration as well. It does not just stop at the area that is facing the direction you threw the object. Because of friction between the air particles and the object, obviously, the larger the surface area, the more friction and hence resistence. Not to mention, the less laminar the flow of the air around the object, the higher the resistence due to turbulence.

  Ok, I shall stop here.

   

  err... the first part is about giving it initial velocity... not really part of projectile motion, but more of on Newton's 2nd law