If a 100 ,m long train needs 7.2 ,s to cross | vedclass

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(C) Given: Length of the train, $l = 100 \,m$.Time taken to cross the object, $t = 7.2 \,s$.Velocity of the object moving in the opposite direction, $

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(C) Given: Length of the train, $l = 100 \,m$.Time taken to cross the object, $t = 7.2 \,s$.Velocity of the object moving in the opposite direction, $v_o = 5 \,km/h = 5 	imes \frac{5}{18} \,m/s = \frac{25}{18} \,m/s \approx 1.39 \,m/s$.Let the velocity of the train be $v_t = v$.Since the objects are moving in opposite directions, the relative velocity is $v_{	ext{rel}} = v_t + v_o$.The distance covered to cross the object is equal to the length of the train, $l = v_{	ext{rel}} 	imes t$.$100 = (v + \frac{25}{18}) 	imes 7.2$.Dividing by $7.2$: $\frac{100}{7.2} = v + \frac{25}{18}$.$\frac{1000}{72} = v + \frac{25}{18} \Rightarrow \frac{125}{9} = v + \frac{25}{18}$.$v = \frac{250}{18} - \frac{25}{18} = \frac{225}{18} = 12.5 \,m/s$.Converting to $km/h$: $v = 12.5 	imes \frac{18}{5} = 45 \,km/h$.

If a $100 \,m$ long train needs $7.2 \,s$ to cross an object moving in a direction opposite to the train's direction with a speed of $5 \,km/h$, then find the velocity of the train. (in $\,km/h$)

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