An electrician has to repair an electric fault on a pole of height 4m. He needs to reach a point 1.3m below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use which when inclined at an angle of `60^@` to the horizontal would enable him to reach the required position?

An electrician has to repair an electric fault on a pole of height 5 m. She needs to reach a point 1.3 m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of 60° to the horizontal, would enable her to reach the required position? Also, how far from the foot of the pole should she place the foot of the ladder? (You may take sqrt 3 = 1.73)

A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30^@ to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60^@ to the ground. What should be the length of the slide in each case?

A painter needs to reach the top of a tail sign in the middle of a flat and level field .He uses a ladder of length x to reach a point on the sign 15 feet above the ground . The angle formed where the ladder meets the ground is noted in the figure below as theta , which of the following relation - ships must be true ?

A pole of height 4 m is kept in front of a vertical plane mirror of length 2m. The lower end of the mirror is at a height of 6m form the grown .the horizontal distance betweem the mirror and the pole is 2m. Upto what minimum and maximum heights a man can see the image of top of the pole at a horizontal distance of 4m (from the mirror O standing on the same horizontal line which is passing through the pole and the horizontal point below the mirror?

With reference to the given figure, a man stands on the ground at point A, Which is on the same horizontal plane as B, the foot of the vertical pole BC. The height of the pole is 10 m . The man's eye is 2 m above the ground. He observes the angle of elevation of C, the top of the pole, as x^(@) , where tan x^(@) = (2)/(5) . Calculate : angle of elevation of the top of the pole when he is standing 15 metres from the pole. Give your answer to the nearest degree.

A man swims from a point A on the bank of a river if width 100 m . When he swims perpendicular to the water current, he reaches the other bank 50 m downstream. The angle to the bank at which he should swim, to reach the directly opposite point B on the other bank is. .

small block of mass 200 g is kept at the top of a frictionless incline which is 10 m long and 3.2 m high. How much work was required a. to lift the block from the ground nd put it at the top b. to side the block up the incline? What will be the speed of the block when it reaches the ground if, c. it falls off the incline and drops vertically on the ground d. it slides down the incline? Take g=10 m/s^2 .

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30^0 . After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60^0 . Then the time taken (in minutes) by him, from B to reach the pillar, is : (1) 6 (2) 10 (3) 20 (4) 5

An inquistive student, determined to test the law of gravity for himself, walks to the top of a building og 145 floors, with every floor of height 4 m, having a stopwatch in his hand (the first floor is at a height of 4 m from the ground level). From there he jumps off with negligible speed and hence starts rolling freely. A rocketeer arrives at the scene 5 s later and dives off from the top of the building to save the student. The rocketeer leaves the roof with an initial downward speed v_0 . In order to catch the student at a sufficiently great height above ground so that the rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by rocketeer's jet pack, which he turns on just as he catches the student, before the rocketeer is in free fall. To prevent any discomfort to the student, the magnitude of the acceleration of the rocketeer and the student as they move downward together should not exceed 5 g. Just as the student starts his free fall, he presses the button of the stopwatch. When he reaches at the top of 100th floor, he has observed the reading of stopwatch as 00:00:06:00. What should be the initial downward speed of the rocketeer so that he catches the student at the top of 100 the floor for safe landing ?

The angle of elevation of the top of a tower as observed from a point in a horizontal plane through the foot of the tower is 32^0dot When the observer moves towards the tower a distance of 100m, he finds the angle of elevation of the top to be 63^0dot Find the height of the tower and the distance of the first position from the tower. [Take tan32^0=06248a n dtan63^0=1. 9626]