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A man is sitting on the shore of a river. He is in the line of 1.0 m long boat and is 5.5 m away from the centre of the boat. He wishes to throw an apple into the boat. If he can throw the apple only with a speed of 10 m/s, find the minimum and maximum angles of projection for successful shot. Assume that the point of projection and the edge of the boat are in the same horizontal level.
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A river 400 m wide is flowing at a rate of 2.0 m/s. A boat is sailing at a velocity of 10 m/s with respect to the water, in a direction perpendicular to the river. Find the time taken by the boat to reach the opposite bank.
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A river 400 m wide is flowing at a rate of 2.0 m/s. A boat is sailing at a velocity of 10 m/s with respect to the water, in a direction perpendicular to the river. How far from the point directly opposite to the starting point does the boat reach the opposite bank?
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A swimmer wishes to cross a 500 m wide river flowing at 5 km/h. His speed with respect to water is 3 km/h. If he heads in a direction making an angle θ with the flow, find the time he takes to cross the river.
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A swimmer wishes to cross a 500 m wide river flowing at 5 km/h. His speed with respect to water is 3 km/h. Find the shortest possible time to cross the river.
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Consider the situation of the previous problem. The man has to reach the other shore at the point directly opposite to his starting point. If he reaches the other shore somewhere else, he has to walk down to this point. Find the minimum distance that he has to walk.
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An aeroplane has to go from a point A to another point B, 500 km away due 30° east of north. A wind is blowing due north at a speed of 20 m/s. The air-speed of the plane is 150 m/s. Find the direction in which the pilot should head the plane to reach the point B.
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An aeroplane has to go from a point A to another point B, 500 km away due 30° east of north. A wind is blowing due north at a speed of 20 m/s. The air-speed of the plane is 150 m/s. Find the time taken by the plane to go from A to B.
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Two friends A and B are standing a distance x apart in an open field and wind is blowing from A to B. A beat a drum and B hears the sound t1 time after he sees the event. A and B interchange their positions and the experiment is repeated. This time B hears the drum timer after he sees the event. Calculate the velocity of sound in still air v and the velocity of wind u. Neglect the time light takes in travelling between the friends.
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Suppose A and B in the previous problem change their positions in such a way that the line joining them becomes perpendicular to the direction of wind while maintaining the separation x. What will be the time B finds between seeing and hearing the drum beating by A?
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Six particles situated at the corner of a regular hexagon of side a move at a constant speed v. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet each other.
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The weight of a body at the poles is greater than the weight at the equator. Is it the actual weight or the apparent weight we are talking about? Does your answer depend on whether only the earth's rotation is taken into account or the flattening of the earth at the poles is also taken into account?
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Consider a planet in some solar system which has a mass double the mass of the earth and density equal to the average density of the earth. An object weighing W on the earth will weight
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Let \[\overrightarrow A\] be a unit vector along the axis of rotation of a purely rotating body and \[\overrightarrow B\] be a unit vector along the velocity of a particle P of the body away from the axis. The value of \[\overrightarrow A.\overrightarrow B\] is ____________ .
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The time taken by Mars to revolve round the Sun is 1.88 years. Find the ratio of average distance between Mars and the sun to that between the earth and the sun.
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The moon takes about 27.3 days to revolve round the earth in a nearly circular orbit of radius 3.84 × 105 km/ Calculate the mass of the earth from these data.
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Let \[\overrightarrow F\] be a force acting on a particle having position vector \[\overrightarrow r.\] Let \[\overrightarrow\Gamma\] be the torque of this force about the origin, then __________ .
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Two small balls, each of mass m are connected by a light rigid rod of length L. The system is suspended from its centre by a thin wire of torsional constant k. The rod is rotated about the wire through an angle θ0 and released. Find the force exerted by the rod on one of the balls as the system passes through the mean position.
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The energy of a given sample of an ideal gas depends only on its
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In Regnault's apparatus for measuring specific heat capacity of a solid, there is an inlet and an outlet in the steam chamber. The inlet is near the top and the outlet is near the bottom. Why is it better than the opposite choice where the inlet is near the bottom and the outlet is near the top?
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