(^410) A Textbook of Engineering Mechanics
(a) Actual velocity diagram (b) Relative velocity diagram
Fig. 19.10.
First of all, let us draw the actual velocity diagram of the train and object as shown in Fig.
19.10. (a). Now draw the relative velocity diagram as shown in Fig. 19.10 (b) and as discussed
below :
- First of all, draw a line XL representing the actual direction of the motion of the train with
a velocity of 52 km.p.h. - Now cut off XM equal to 52 km to some suitable scale on the opposite direction of the
actual motion of the train. - Now cut off XN equal to 39 km to the scale at right angle to LM, which represents the
actual velocity with which the object is running away. - Complete the parallelogram XMRN with XM and XN as adjacent sides.
- Join XR which gives the magnitude and direction of the relative velocity. By measurement,
we find that ∠ θ = 36.9° and XR = 65 km. p.h. = 18.1 m/s
Now let us draw the muzzle velocity diagram as shown in Fig. 19.11. and as discussed below:
Fig. 19.11.- First of all, draw the relative velocity diagram and the parallelogram XMRN as discussed
above. - Cut off XQ equal to 18.1 m (i.e. relative velocity of train and object) to some suitable
scale. - At X draw a line at an angle of 30°, which represents the line connecting the man and
object with the train. - Now cut off QP equal to 200 m to the scale and join QP. Now P represents the position of
the object, which the rifleman wants to hit. - Now let the rifleman make an angle α with the train in order to hit the object as shown in
Fig. 19.11.