A rat is moving down the slant of a wedge of angle of inclination θ with a velocity v → as shown in the figure. If the wedge moves towards left with a velocity u → , find (a) velocity of the rat relative to ground, (b) value of θ , if the rate moves vertically downward relative to an observer G fixed with the ground.

Given; Velocity of rat relative to wedge v → R , W = v → Velocity of wedge v → W = u → (a) The velocity of rat R relative to the person G standing on ground v → R , W = v → R - v → W ⇒ v → R = v → R , W + v → W = u → + v → v R = u 2 + v 2 + 2 u v cos 180 ° - θ = u 2 + v 2 - 2 u v cosθ (b) If the rat appears to move vertically downward relative to G , then, u = v cos θ ⇒ cos θ = u v ⇒ θ = cos - 1 u v

A rat is moving down the slant of a wedge of angle of inclination θ with a velocity v → as shown in the figure. If the wedge moves towards left with a velocity u → , find (a) velocity of the rat relative to ground, (b) value of θ , if the rate moves vertically downward relative to an observer G fixed with the ground.

Given; Velocity of rat relative to wedge v → R , W = v → Velocity of wedge v → W = u → (a) The velocity of rat R relative to the person G standing on ground v → R , W = v → R - v → W ⇒ v → R = v → R , W + v → W = u → + v → v R = u 2 + v 2 + 2 u v cos 180 ° - θ = u 2 + v 2 - 2 u v cosθ (b) If the rat appears to move vertically downward relative to G , then, u = v cos θ ⇒ cos θ = u v ⇒ θ = cos - 1 u v

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JEE Advanced

IMPORTANT

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A rat is moving down the slant of a wedge of angle of inclination $θ$ with a velocity $\vec{v}$ as shown in the figure. If the wedge moves towards left with a velocity $\vec{u}$ , find

(a) velocity of the rat relative to ground,
(b) value of $θ$ , if the rate moves vertically downward relative to an observer $G$ fixed with the ground.

Important Questions on Kinematics II

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.45

A truck is moving a constant velocity of $u = 54 km h^{- 1}$ . In what direction should a stone be projected up with a velocity of $v = 30 m s^{- 1}$ , from the floor of the truck, so as to appear at right angles to the truck, for a person standing on earth?

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MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.46

A block slips along an incline of a wedge. Due to the reaction of the block on the wedge, it slips backwards. An observer on the wedge will see the block moving straight down the incline. Discuss how to find the absolute velocity of the block.

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MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.47

A political party has to start its procession in an area where wind is blowing at a speed of

30 \sqrt{2} km h^{- 1}

and party flags on the cars are fluttering along north-east direction. If the procession starts with a speed of

40 km h^{- 1}

towards north, find the direction of flags on the cars.

MEDIUM

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.48

A bird is flying due east with a velocity of

4 {m s}^{- 1}

. The wind starts to blow with a velocity of

3 {m s}^{- 1}

due north. What is the magnitude of relative velocity of bird with respect to wind? Find out its direction also.

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.49>Q (a)

A man can row a boat

4 km h^{- 1}

in still water. He is crossing a river where the current is

2 km h^{- 1}

.
(a) In what direction will his boat be headed if he wants to reach a point on the other bank, directly opposite to starting point?
(b) If width of the river is

4 km

, how long will it take him to cross the river with the condition in part

a

?
(c) In what direction should he head the boat if he wants to cross river in shortest time. Find the time taken by him to cross the river? Also find the location of the point where he lands on the other side of the river.

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.50

A man wishes to cross a river in a boat. If he crosses the river in minimum time, he takes

10

\min

with a drift of

120 m

. If he crosses the river taking the shortest route, he takes

12.5 \min

. Find the velocity of the boat with respect to water.

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.51>Q (a)

A man can swim at a rate of

5 km h^{- 1}

in still water. A

1 km

wide river flows at the rate of

3 km h^{- 1}

. The man wishes to swim across the river directly opposite to the starting point.
(a) Along which direction must the man swim?
(b) What should be his resultant velocity?
(c) How much time will he take to cross the river?

HARD

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.52

The ratio of the distance carried away by the water current downstream in crossing a river by a person making same angle with downstream and upstream are, respectively,

2 : 1

. Show that the ratio of the speed of the person to water current cannot be less than

\frac{1}{3}

Important Questions on Kinematics II

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