Question

ur me velocity (KV“). If it falls through distance'x' and possesses a velocity 'V' at that
2 kx
instant, prove that --
, where mg = Ka?.
m
6. A body of mass falls from rest under gravity in a fluid whose resistance to motion at any instant is mk
time its velocity, where K is constant. Find the terminal velocity of the body and also the time taken to
acquire one-half of its limiting speed.
-2gx
7.
The x descended by a parachuter satisfies the differential equati
e k²
where 'k'
dt
and 'g' are constants and x=0 when t=0.show that
8. A body of mass 'm' falls from rest under influence of gravity and a retarding force due to air resistance
proportional to square of velocity. Find the velocity and distance described as a function of time.
Hence, show that the velocity of the body approaches the limiting value.
9.
A particle of unit mass .noves in a horizontal straight line OA with in acceleration
5 at a distance r and
directed towards 0.If initially the particle was at rest at a distance a from 0,show that it will be a distance
from 0 at the end of time a 3.
2
V
10. Assuming that the resistance to movement of a ship through water in the form of (a? + b2 v2), where v
is the velocity, a and b are constants, write down the differential equation for retardation of ship
moving with engine stopped. Prove that the time in which the speed falls to one half its original value
abu
u is given by
tan- Go2m2), where w is the length of the ship.
abg
11. A particle of mass m is projected vertically upward with velocity Vo. Assuming that the air resistance is k​

Answer 1

Answer:

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