Engineering Mechanics

Chapter 24 : Laws of Motion „„„„„ 497

Example 24.20. Two men, standing on a floating boat, run in succession, along its length,
with a speed of 4.2 m/sec relative to the boat and dive off from the end. The weight of each man is
80 kg and that of the boat is 400 kg. If the boat was initially at rest, find the final velocity of the boat.
Neglect water friction.

Solution. Given : v = 4.2 m/sec ; Weight of each man, w = 80 kg-wt (in gravitational units)
or m = 80 kg (in absolute units) ; Weight of boat = 400 kg-wt (in gravitational units) or M = 400 kg
(in absolute units).

Let V = Velocity of the boat after the second man dives off the boat.
A little consideration will show, that when the first man dives off the boat, it will give some
momentum to the boat as well as the second man (who is still standing on the boat). When the second
man also dives off the boat, it will also give some momentum to the boat. Therefore the total momentum
gained by the boat is equal to the momentum given by the first man plus the momentum given by the
second man to the boat.

Now final momentum of the boat

= 400 V kg m/s ...(i)

and momentum given by the first man to the boat

= 80 × 4.2 = 336 kg-m/s

Similarly, momentum given by the second man to the boat

= 80 × 4.2 = 336 kg-m/s

We know that the final momentum of the boat

= Momentum given by the first man

+ Momentum given by the second man

= 336 + 336 = 672 kg-m/s ...(ii)

Now equating equations (i) and (ii),

400 V = 672

∴

672

1.68 m/s

400

V== Ans.

EXERCISE 24.3

1. A bullet of 10 gm mass is fired horizontally with a velocity of 1000 m/s from a gun of
   mass 50 kg. Find (a) velocity with which the gun will recoil, and (b) force necessary to be
   ring the gun to rest in 250 mm. (Ans. 0.2 m/s ; 4 N)


2. A block of mass 10 kg slides over a frictionless horizontal plane with a constant velocity
   of 5 m/s. After some distance, the plane is inclined at an angle of 20º with the horizontal.
   Find the distance through which the block will slide upwards on the inclined plane before
   coming to rest. (Ans 36.5 m)

24.13. MOTION ON INCLINED PLANES

In the previous articles, we have been discussing the motion of bodies on level surface. But
sometimes, the motion of body takes place down or up an inclined plane as shown in
Fig. 24.4 (a) and (b).