A beacon makes one revolution every 10 seconds. It is located on a ship which is anchored 5 km from a straight shore line. How fast is the beam moving along the shore line when it makes an angle of `45^(@)` with the shore?

The slope of the line which makes an angle 45 with the line 3x-y=-5 are

The slopes of the lines which make an angle 45^(@) with the line 3x - y = -5 are

A plumb bob is hung from the ceiling of a train compartment. If the train moves with an acceleration a along a straight horizontal track, the string supporting the bob makes an angle tan^1 (a/g) with the normal to the ceiling. Suppose the train moves on an inclined straight track with uniform velocity, if the angle of incline is tan^-1(a/g) , the string again makes the same angle with the normal to the ceiling. Can a person sitting inside the compartment tell by looking at the plumb line whether the train is accelerated on a horizontal straight track or it is going on an incline? If yes, how? If no, suggest a method to do so.

Read the following paragraph carefully and answer the following: Tie a stone to one end of a string. Take the other end in your hand and rotate the string so that the stone moves along a circle. As long as we are holding the string, we are pulling the stone towards us i.e. towards the centre of the circle and are appliying a force towards it. The force stops acting on it if we release the string. In this case, the stone will fly off along a straight line which is the tangent to the circle at the position of the stone when the string is released, because that the directionn of its velocity at that instant of time. You may recall a similar activity in which a 5 rupee coin kept on a rotating circular disc flies off the disc along the tangent to the disc. Thus, a force acts on any object moving along a circle and it is directed towards the centre of the circle. This is called the Centripetal force. The impressed force on the same is in which direction?

Read the following paragraph carefully and answer the following: Tie a stone to one end of a string. Take the other end in your hand and rotate the string so that the stone moves along a circle. As long as we are holding the string, we are pulling the stone towards us i.e. towards the centre of the circle and are appliying a force towards it. The force stops acting on it if we release the string. In this case, the stone will fly off along a straight line which is the tangent to the circle at the position of the stone when the string is released, because that the directionn of its velocity at that instant of time. You may recall a similar activity in which a 5 rupee coin kept on a rotating circular disc flies off the disc along the tangent to the disc. Thus, a force acts on any object moving along a circle and it is directed towards the centre of the circle. This is called the Centripetal force. What happens if the string is released?

Read the following paragraph carefully and answer the following: Tie a stone to one end of a string. Take the other end in your hand and rotate the string so that the stone moves along a circle. As long as we are holding the string, we are pulling the stone towards us i.e. towards the centre of the circle and are appliying a force towards it. The force stops acting on it if we release the string. In this case, the stone will fly off along a straight line which is the tangent to the circle at the position of the stone when the string is released, because that the directionn of its velocity at that instant of time. You may recall a similar activity in which a 5 rupee coin kept on a rotating circular disc flies off the disc along the tangent to the disc. Thus, a force acts on any object moving along a circle and it is directed towards the centre of the circle. This is called the Centripetal force. What is centripetal force?

Find the equation of the lines make an angle 60^@ with positive x-axis and at a distance 5sqrt2 units measured from the point (4,7) along the line x–y+3=0.

Suppose that there are two cell phone towers within range of a cell phone. The two towers are located at 6km apart along a straight highway. Running east to west and the cell phone is north of the highway. The signal is 5km from the first tower and sqrt31 km from the second tower. Determine the position of the cell phone north and east of the first tower and how far it is from the highway.