1.95. Find the magnitude and direction of the force acting on the
particle of mass in during its motion in the plane xy according to the
law x = a sin cot, y = b cos cot, where a, b, and co are constants.
1.96. A body of mass in is thrown at an angle to the horizontal
with the initial velocity v 0. Assuming the air drag to be negligible,
find:
(a) the momentum increment Op that the body acquires over the
first t seconds of motion;
(b) the modulus of the momentum increment ip during the total
time of motion.
1.97. At the moment t = 0 a stationary particle of mass in expe-
riences a time-dependent force F = at (r — t), where a is a constant
vector, r is the time during which the given force acts. Find:
(a) the momentum of the particle when the action of the force dis-
continued;
(b) the distance covered by the particle while the force acted.
1.98. At the moment t = 0 a particle of mass m starts moving due
to a force F = F, sin cot, where F 0 and co are constants. Find the
distance covered by the particle as a function of t. Draw the approx-
imate plot of this function.
1.99. At the moment t = 0 a particle of mass m starts moving due
to a force F = F, cos cot, where F, and co are constants. How long
will it be moving until it stops for the first time? What distance will
it traverse during that time? What is the maximum velocity of the
particle over this distance?
1.100. A motorboat of mass m moves along a lake with velocity v 0.
At the moment t = 0 the engine of the boat is shut down. Assuming
the resistance of water to be proportional to the velocity of the boat
F = —rv, find:
(a) how long the motorboat moved with the shutdown engine;
(b) the velocity of the motorboat as a function of the distance cov-
ered with the shutdown engine, as well as the total distance covered
till the complete stop;
(c) the mean velocity of the motorboat over the time interval
(beginning with the moment t = 0), during which its velocity de-
creases it times.
1.101. Having gone through a plank of thickness h, a bullet
changed its velocity from v, to v. Find the time of motion of the
bullet in the plank, assuming the resistance force to be proportional
to the square of the velocity.
1.102. A small bar starts sliding down an inclined plane forming
an angle cc with the horizontal. The friction coefficient depends on
the distance x covered as k = ax, where a is a constant. Find the
distance covered by the bar till it stops, and its maximum velocity
over this distance.
1.103. A body of mass m rests on a horizontal plane with the fric-
tion coefficient lc. At the moment t = 0 a horizontal force is applied
to it, which varies with time as F = at, where a is a constant vector.
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