APT ACADEMIC SOLUTIONS : APT ACADEMIC SOLUTIONS
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Slide 3 : www.aptacads.com Kinematics - 2 Session
Slide 4 : www.aptacads.com Position of A w.r.t. B: Since velocity is defined as the time derivative of position, we have Relative velocity
Example : www.aptacads.com Example A river is flowing at a speed of 2 m/s. There is a boat in the river which can move in still water at 10 m/s.
Find the time taken by the boat to travel 100 m downstream when its engine is off?
Find the time taken by the boat to travel 100 m upstream when its engine is on?
If the engine is off, find the speed of the boat as observed by a stationary observer on the river bank?
When the engine is on and the boat is moving in a direction opposite to that of the flow of the river, find its velocity as observed by a stationary observer on the banks?
Solution : www.aptacads.com Solution When the engine is off, the boat flows with the river. Hence,
Velocity as observed from ground = 2 m/s
Time taken to travel 100m downstream = 100/2 = 50 s.
With the engine on, when it travels upstream,
speed = 10 – 2 = 8 m/s.
Time taken to travel 100 m upstream = 100/8 = 12.5 s.
Example : www.aptacads.com Example A boat can travel at a speed of 10 m/s in still water. Find the orientation of the boat such that it reaches point B, directly opposite to B across the river.
Solution : www.aptacads.com Solution There are three entities –
B – Boat; R – River; G - Ground
Example : www.aptacads.com Example A man who can swim at a speed of vm relative to “still” water decides to cross a river with water flowing at a speed vr (vr < vm) such that he “orients” his swimming at an angle ‘q’ to the perpendicular across the river as shown in the figure. Find the time taken by him to across the river as a function of ‘q’, given that the width of the river is ‘d’ and calculate the minimum possible time in which he can “across” the river.
Solution : www.aptacads.com Solution Three entities: man, river, ground. Seen from the ground, the man swims at an angle f w.r.t. the y-axis. If the man takes time t to cross the river, then t is minimum when cos q is maximum (= 1). Hence,
Example : www.aptacads.com Example
Solution : www.aptacads.com Solution There are three entities –
M – Man; R – Rain; G - Ground Since the man finds the raindrops striking vertically down,
Example (Important) : www.aptacads.com Example (Important)
Solution : www.aptacads.com Solution Position of ball w.r.t. trolley:
Solution : www.aptacads.com Since the ball eventually hits the trolley, hence Since the initial position vector of A is equidistant from the x and y axes, Solution
Solution : www.aptacads.com Solution
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