Monday

October 20, 2014

October 20, 2014

Posted by **Jake** on Thursday, October 25, 2012 at 10:23pm.

Assume that the rate at which mass is expelled is given by dm/dt=mk, where m is the instantaneous mass of the rocket and k is a cosntant, and that the rocket is retarded by air resistance with a force bv where b is a constant. find the velocity of the rocket as a function of time.

I have worked it down to the last step but am having trouble finishing the integration to find v(t).

F_net = F_thrust - F_grav - F_air.resist

ma = (dp/dt) - mg - bv

(dv/dt) = (uk - g) - (bv/m)

m = m_o*e^kt ---> not sure if this part is right??

so (dv/dt) = (uk - g) - b*m_o*e^-kt*v

v = dx/dt so multiply by dt to get the integration equation of:

dv = (uk-g)dt - b*m_o*e^-kt*dx

my attempt so far:

v(t) = (uk-g)t - ????

***I am stuck on integrating the:

b*m_o*e^-kt*dx

- Physics -
**Jake**, Thursday, October 25, 2012 at 10:26pmI think that the answer comes out to be

v(t)=(uk-g)t - b*m_o*(e^-kt)*x(t)

- Physics -
**Jake**, Thursday, October 25, 2012 at 10:28pmbecause b and m_o are constants and i believe that e^-kt is taken as a constand as well. Leaving dx to be integrated between 0 and x(t).

am i correct? more opinions welcomed please

**Answer this Question**

**Related Questions**

Physics - A rocket whish is in deep space and initially at rest relative to an ...

physics - Model rocket engines are sized by thrust, thrust duration, and total ...

Physics - Consider a rocket in space that ejects burned fuel at a speed of vex= ...

PHYSICS(elena) - Consider a rocket in space that ejects burned fuel at a speed ...

PHYSICS IMP PLS - Consider a rocket in space that ejects burned fuel at a speed ...

Classical Mechanics Physics - Consider a rocket in space that ejects burned fuel...

physics - A rocket has an exhaust gas velocity of 2329 m/s and an expelled gas ...

physics Classical Mechanics - Consider a rocket in space that ejects burned fuel...

physics - A rocket of total mass 2580 kg is traveling in outer space with a ...

physic - Consider a rocket in space that ejects burned fuel at a speed of 1.5 km...