Question 144: Laws of Motion

Question

A spaceship in space sweeps stationary
interplanetary dust. As a result, its mass
increases at a rate $${{dM\left( t \right)} \over {dt}}$$ = bv
2
(t), where v(t) is
its instantaneous velocity. The instantaneous
acceleration of the satellite is :

Accepted Answer

Given $${{dM\left( t \right)} \over {dt}}$$ = bv
2
(t)
In free space
no external force
so there in only thrust force on rocket.
F
thrust
= v$${{dm} \over {dt}}$$
Force on satellite = $$ - \overrightarrow v {{dm\left( t \right)} \over {dt}}$$
M(t)a = Ã¢ÂÂ v (bv
2
)
$$ \Rightarrow $$ a = $$ - {{b{v^3}} \over {M\left( t \right)}}$$

Answer

-bv
3
(t)

Answer

$$ - {{2b{v^3}} \over {M\left( t \right)}}$$

Answer

$$ - {{b{v^3}} \over {M\left( t \right)}}$$

Answer

$$ - {{b{v^3}} \over {2M\left( t \right)}}$$

Laws of Motion

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate ${{dM\left( t \right)} \over {dt}}$ = bv 2 (t), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :

Choose the correct answer: