Engineering Mechanics

(^374) „„„„„ A Textbook of Engineering Mechanics
This is a quadratic equation in t.
∴

• 24.9 (24.9) – 4^2 4.9 (– 20)
  0.71 s
  2 4.9

t

±××

==

×

Ans.

Example 17.24. Two particles A and B are dropped simultaneously from rest two points

both 100 m above the ground. Particle A falls on the ground, while the particle B in its mid path, hits

a fixed plane inclined to the horizontal as shown in the Fig. 17.3.

Fig. 17.3.

As a result of this impact, the direction of its velocity becomes horizontal. Compare the times

of fall of the particles A and B to reach the ground.

Solution. First of all, consider motion of the stone A (i.e. from A to C). In this case, initial

velocity (u 1 ) = 0 (because it is dropped ) and distance (s 1 ) = 100 m

Let t 1 = Time taken by the particle A to reach C.

We know that distance travelled by the stone A (s 1 )

222

11

11

100 0 9.8 4.9

22

=+ut gt =+×t =t

∴ 1

100

4.52 s

4.9

t ==

Now consider motion of the stone B (first from B to D).

In this case, initial velocity (u 2 ) = 0 (because it is dropped ) and distance (s 2 ) = 50 m

Let t 2 = Time taken by the particle B to reach D.

We know that the distance travelled by the stone B (s 2 )

222

22

11

50 0 9.8 4.9

22

=+ut gt =+×t =t

∴ 2

50

3.19 s

4.9

t == ...(ii)

Now consider motion of the stone B (from D or E to F).

Since the direction of the particle B, after impact at D, becomes horizontal, therefore its

velocity in the vertical direction becomes zero. A little consideration will show that the particle B will

take another 3.19 sec to reach from D to F. Therefore total time taken by the particle B to reach F will

be T = 3.19 + 3.19 = 6.38 sec. Therefore ratio of the two times,

1

6.38

1.41

4.52

T

t

== Ans.

Example 17.25. A cage descends in a mine shaft with an acceleration of 0.5 m/s^2. After the

cage has travelled 25 m, a stone is dropped from the top of the shaft. Determine the (a) time taken by

the stone to hit the cage, and (b) distance travelled by the cage before impact.