Home
Class 12
MATHS
A man observes when he has climbed up 1/...

A man observes when he has climbed up `1/3` of the length of an inclined ladder, placed against a wall, the angular depression of an object on the floor is `alphadot` When he climbs the ladder completely, the angleof depression is `beta` . If the inclination of the ladder to the floor is `theta,` then prove that `cottheta=(3cotbeta-cotalpha)/2`

Text Solution

Verified by Experts

The correct Answer is:
`cot^(-1)[(3cot beta - cotalpha)/2]`
Promotional Banner

Similar Questions

Explore conceptually related problems

A man observe that was he has climbed up 1/3 of the length of an inclined ladder ,placed against a wall the angular depression of an object on the floor is alpha and that after he reached the top of the ledder , the angular depression beta If the inclintaion of the ladder to the is theta then prove that cot theta=(3 cot beta-cot alpha)/2

A man observes that when he moves up a distance c metres on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is 30^0, and when he moves up further a distance c metres, the angle of depression of that point is 45^0dot The angle of inclination of the slope with the horizontal is.

A ladders is more likely to slip when a person is near the top than when he is near the bottom. The friction between the ladder and floor decreases as he climbs up.

A uniform ladder of length 3.25 m and weight 250 N is placed against a smooth vertical wall with its lower end 1.25 m from the wall. If coefficient of friction between the ladder and the floor is 0.3, then, find the frictional force acting on the ladder at the point of contact between ladder and floor.

A rod of length 'l' is inclined at an angle 'theta' with the floor against a smooth vertical wall. If the end A moves instantaneously with velocity v_(1) , what is the velocity of end B at the instant when rod makes 'theta' angle with the horizontal.

A ladder is inclined to a wall making an angle of 30° with it. A man is ascending the ladder at the rate of 3 m/sec. How fast is he approaching the wall ?

A ladder makes an angle of 60^0 with the ground when placed against a wall. If the foot of the ladder is 2m away from the wall, then the length of the ladder (in metres) is (a) 4/(sqrt(3)) (b) 4/(sqrt(3)) (c) 2sqrt(2) (d) 4

A uniform ladder of length L and mass m_(1) rests against a frictionless wall. The ladder makes an angle theta with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when a firefighter of mass m_(2) is a distance x from the bottom. (b) If the ladder is just on the verge of slipping when the firefighter is a distance d from the bottom, what is the coefficient of static friction between ladder and ground?

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 ladder AP of length 5m inclined to a vertical wall is slipping over a horizontal surface with velocity of 2m//s , when A is at distance 3m from ground. What is the velocity of COM at this moment?