#
On a long horizontally moving belt
(Fig. 3.26), a child runs to and fro with a speed 9 km h^{-1} (with
respect to the belt) between his father and mother located 50 m apart on the
moving belt. The belt moves with a speed of 4 km h^{-1}. For an
observer on a stationary platform outside, what is the

# (a) speed of the child running in the direction of motion of the belt ?.

# (b) speed of the child running opposite to the direction of motion of the belt ?

# (c) time taken by the child in (a) and (b) ?

# Which of the answers alter if motion is viewed by one of the parents?

# Answer:

(a) Speed of the belt, vB = 4 km/h

Speed of the boy, vb = 9 km/h

Speed of the boy, vb = 9 km/h

Since the boy is running
in the same direction of the motion of the belt, his speed (as observed by the stationary observer) can
be obtained as:

vbB = vb + vB = 9 + 4 = 13 km/h

vbB = vb + vB = 9 + 4 = 13 km/h

(b) Since the boy is
running in the direction opposite to the direction of the motion of the belt,
his speed (as observed by the stationary observer) can be obtained as:

vbB = vb + (- vB) = 9 - 4 = 5 km/h

vbB = vb + (- vB) = 9 - 4 = 5 km/h

(c) Distance between the child’s parents = 50
m

As both parents are
standing on the moving belt, the speed of the child in either direction as
observed by the parents will remain the same i.e., 9 km/h = 2.5 m/s.

Hence, the time taken by
the child to move towards one of his parents is

(d) If the motion is
viewed by any one of the parents, answers obtained in (a) and

(b) get altered. This is
because the child and his parents are standing on the same belt and hence, are
equally affected by the motion of the belt. Therefore, for both parents
(irrespective of the direction of motion) the speed of the child remains the same i.e., 9 km/h.

For this reason, it can
be concluded that the time taken by the child to reach any one of his parents remains unaltered.

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