1 ) A boat which has speed of 5 km / h in still water across a river of width of 1km along the shortest path in 15 minutes . The velocity of river in km / s is : -
A ) 3 km / h , B ) 7 km / h ,
C ) 18 km / h , D ) 21 km / h ,
Correct Answer : - A ) 3 km / h ,
Solution : -
Let the velocity of river be ‘x’ km / hr .
Speed of boat = 5 km / h , And
Width of river ( AB ) = 1 km / hr .
Time taken to cross the river by boat = 15 minutes .
So distance covered by boat : - d = v t ,
d = 5 x 15 / 60 = 1.25 km / hr .
Now , AB = 1 km / hr , And AC = 1.25 km / hr .
And angle β = 90° .
So ,
( AB ) ^ 2 + ( BC ) ^ 2 = ( AC ) ^ 2 ,
1 + ( BC ) ^ 2 = ( 1.25 ) ^ 2 ,
So , BC = 0.75 km .
So , distance covered by river water in 15 minutes is 0.75 km / hr .
Velocity of river : - v = d / t = 0.75 / (1/4) ,
v = 3 km / h , Answer .
2 ) The velocity time graph of a car is moving along a straight road is shown in figure . The average velocity of car in first 25 seconds is : -
Choose single option from these following : -
A ) 5 m / s , B ) 10 m / s ,
C ) 14 m / s , D ) None of these ,
Correct Answer : - C ) 14 m / s ,
Solution : -
3 ) The velocity – time graph for particle is moving in a straight line . The sum of two shaved areas represents : -
A ) increase in displacement of a particle ,
B ) the average velocity of a particle ,
C ) average acceleration of particle ,
D ) the distance moved by a particle ,
Correct Answer : - D ) the distance moved by a particle ,
Solution : -
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