18%20-%20Dynamics%20_%20Applications%20of%20Derivative%20_

18%20-%20Dynamics%20_%20Applications%20of%20Derivative%20_...

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PROBLEMS 18 - DYNAMICS ( APPLICATIONS OF Derivatives ) Page 1 ( 1 ) A particle executing rectilinear motion travels distance x cm in t seconds where x = 2t 3 - 9t 2 + 5t + 8. Find its velocity at a time when its acceleration is 18 cm / s 2 . [ Ans: 5 cm / s ] ( 2 ) River flows from east to west. A sailor, trying to cross the river, tries to row the boat with a velocity four times the velocity of stream of the river in a direction 60 ° west of north, but due to the drag force of the river travels along the direction making some angle east of north. If he takes 60 minutes to cross the river, what time would he take in moving the distance equal to the width of the river in the direction of the stream ? [ Ans: 24 minutes ] ( 3 ) A particle is given four velocities, 3 cm / s towards the east, 8 cm / s towards 30 ° north of east, 8 cm / s towards 60 ° west of north and 4 cm / s towards the south directions. Find the resultant velocity of the particle. [ Ans: 5 cm / s ] ( 4 ) Two boats, A and B, both sailing at 13 km / hr are trying to cross a river flowing at 12 km / hr. Boat A moves along the shortest path and boat B moves along a path of shortest time. Find the ratio of time taken by boat A to that taken by boat B in crossing the river. [ Ans: 2.6 ] ( 5 ) A boat takes time t 1 to travel a distance equal to the width of the river upstream the river, time t 2 to travel the same distance downstream the river and time t 3 to cross the river. In all the cases, the boat has a constant speed and the river flows with the same velocity. Prove that t 1 t 2 = t 3 2 . ( 6 ) The particles A and B are at ( - 5, - 5 ) and ( 5, 0 ) in Cartesian co-ordinate system initially. They start moving simultaneously with velocities ( 1, 3 ) and ( - 2, 3 ) units per second respectively. After what time will they be closest to each other and what is the shortest distance between them.
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18%20-%20Dynamics%20_%20Applications%20of%20Derivative%20_...

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