Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
PLZ DERIVE EXPRESSION FOR ROCKET IN HCV I AM NOT UNABLE TO GET IT PLZZZZ ANY OTHER BIT MORE EXPALANATORY
Instantaneous velocity of the rocket. Consider a flight of a rocket directed vertically upwards at time t=0, the mass of the rocket + fuel = m0 and its initial velocity is v0 .
Let v be the upward velocity of the rocket at this time . Momentum at time t=mv
mass of rocket and unburnt fuel will reduce to (m-delta m) at the end of the interval delta t
let the velocity increase to (v + delta v).
momentum of rocket and unburnt fuel at time (t + delta t) = (m - delta m)( v + delta v)
total momentum at time (t + delta t) = (m - delta m)(v + delta v) + m( -v gravitation)
v gravitation is the velocity of the echaust gases with respect to the earth. It is taken as negative becasue gases move in opposite directions. to that of the rocket.
mv = (m - delta m) ( v + delta v) + m ( -v gravitation)
mv = mv + m delta v - v delta m - delta m delta v - v gravitation delta m.
m delta v = delta m ( v + v gravitation) + delta m delta v
the term delta m delta v can be dropped because of its small vale.
m delta v = delta m ( v + v gravitation)
if vr is the resultant velocity of the gases relative to the rocket. then
vr = v gravitation + (-v) = v gravitation - v
vr = -v gravitation - v
negative sign shows that vr is in a downward direction whereas the motion of the rocket is in upward direction.
m delta v = - vr delta m
delta v = - vr (delta m / m)
dv = -vr (dm/m)
integrating we get
v-v0 = -vr [ ln m -ln m0] = -vr ln [m/m0]
v = v0 + vr ln [ m0/m ] ------------------------------------------------------------- (1)
this gives velocity of rocket at any time t when the mass of the unburnt fuel is m
initial velocity v0 = 0 then
v = vr ln [m0/m] ------------------------------------------------------------------------(2)
accelaration of the rocket
differenciation of velocity gives accelaration.
accelaration is inversely propertional to m
Thrust on rocket
F = -vr dm/dt --------------------------------------------------------------------------(3)
Burn out speed.
vb = burn out speed.
vb = v0 + vr log [m0/mc] ------ (4) where mc is the mass of the container containing fuel.
PLEASE APPROVE
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !