Home
Class 12
MATHS
A vertical pole (more than 100 m high) c...

A vertical pole (more than 100 m high) consists of two pottions, the lower being one third of the whole. If the upper portion subtends an angle `tan ^(-1)((1)/(2))` at a point in a horizontal plance through the foot of the pole and distance 40 m from it, then the height of the pole is

A

100m

B

120 m

C

150 m

D

None of these :

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

A pole stands erect on the ground. If the angle of elevation of the top of the pole from a point 90m away from the foot of the pole is 30^(@) , find the height of the pole.

Two poles of equal heights are standing opposite each other on either side of the road, which is 80m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60^(@) and 30^(@) , respectively. Find the height of the poles and the distances of the point from the poles.

An electrician has to repair an electric fault on a pole of height 5m. She needs to reach a point 1.3m below the top of the pole to undertake the repair work (see the given figure). What should be the length of the ladder that she should use which, when inclined at an angle of 60^(@) to teh horizontal, would enable her to reach the required position? Also, how far from the foot of the pole shoudl she place the foot of the ladder? (you may take sqrt3= 1.73 )

A vertical tower PQ subtends th same angle 30^(@) at each of two place A and B, 60 m apart on the ground, AB subtends an angle 120^(@) at the foot of the tower. If h is the height of the tower, then 9h^(2)+h+1 is equal to

One end of a light spring of natural length 4m and spring constant 170 N/m is fixed on a rigid wall and the other is fixed to a smooth ring of mass (1)/(2) kg which can slide without friction in a verical rod fixed at a distance 4 m from the wall. Initially the spring makes an angle of 37^(@) with the horizontal as shown in figure. When the system is released from rest, find the speed of the ring when the spring becomes horizontal.

Two blocks of mass m_(1)=10kg and m_(2)=5kg connected to each other by a massless inextensible string of length 0.3m are placed along a diameter of the turntable. The coefficient of friction between the table and m_(1) is 0.5 while there is no friction between m_(2) and the table. the table is rotating with an angular velocity of 10rad//s . about a vertical axis passing through its center O . the masses are placed along the diameter of the table on either side of the center O such that the mass m_(1) is at a distance of 0.124m from O . the masses are observed to be at a rest with respect to an observed on the tuntable (g=9.8m//s^(2)) . (a) Calculate the friction on m_(1) (b) What should be the minimum angular speed of the turntable so that the masses will slip from this position? (c ) How should the masses be placed with the string remaining taut so that there is no friction on m_(1) .

An electrician wants to repair an electric connection on a pole of height 9 m. He needs to reach 1.8 m below the top of the pole to do repair work. What should be the length of the ladder which he should use, when he climbs it at an angle of 60^(@) with the ground? What will be the distance between foot of the ladder and foot of the pole?

Two small and similar bar magnets have magnetic dipole moment of 1.0 Am^(2) each. They are kept in a plane in such a way that their axes are perpendicular to each other. A line drawn through the axis of one magnet passes through the centre of other magnet. If the distance between their centers is 2 m, find the magnetic field at the mid point of the line joining their centers.

Thin films, including soap bubbles and oil show patterns of alternative dark and bright regions resulting from interference among the reflected light waves. If two waves are in phase, their crests and troughs will coincide. The interference will be constructive and the amplitude of resultant wave will be greater then either of constituent waves. If the two wave are not of phase by half a wavelength (180^(@)) , the crests of one wave will coincide width the troughs of the other wave. The interference will be destructive and the amplitude of the resultant wave will be less than that of either constiuent wave. 1. When incident light I, reaches the surface at point a, some of the light is reflected as ray R_(a) and some is refracted following the path ab to the back of the film. 2. At point b, some of the light is refracted out of the film and part is reflected back through the film along path bc. At point c, some of the light is reflected back into the film and part is reflected out of the film as ray R_(c) . R_(a) and R_(c) are parallel. However, R_(c) has traveled the extra distance within the film of abc. If the angle of incidence is small, then abc is approximately twice the film's thickness . If R_(a) and R_(c) are in phase, they will undergo constructive interference and the region ac will be bright. If R_(a) and R_(c) are out of phase, they will undergo destructive interference and the region ac will be dark. I. Refraction at an interface never changes the phase of the wave. II. For reflection at the interfere between two media 1 and 2, if n_(1) gt n_(2) , the reflected wave will change phase. If n_(1) lt n_(2) , the reflected wave will not undergo a phase change. For reference, n_(air) = 1.00 . III. If the waves are in phase after reflection at all intensities, then the effects of path length in the film are: Constrictive interference occurs when 2 t = m lambda // n, m = 0, 1,2,3 ,... Destructive interference occurs when 2 t = (m + (1)/(2)) (lambda)/(n) , m = 0, 1, 2, 3 ,... If the waves are 180^(@) out of the phase after reflection at all interference, then the effects of path length in the film area: Constructive interference occurs when 2 t = (m + (1)/(2)) (lambda)/(n), m = 0, 1, 2, 3 ,... Destructive interference occurs when 2 t = (m lambda)/(n) , m = 0, 1, 2, 3 ,... 72. A film with index of refraction 1.50 coats a glass lens with index of refraction 1.80. What is the minimum thickness of the thin film that will strongly reflect light with wavelength 600 nm?

A circus wishes to develop a new clown act. Fig. (1) shows a diagram of the proposed setup. A clown will be shot out of a cannot with velocity v_(0) at a trajectory that makes an angle theta=45^(@) with the ground. At this angile, the clown will travell a maximum horizontal distance. The cannot will accelerate the clown by applying a constant force of 10, 000N over a very short time of 0.24s . The height above the ground at which the clown begins his trajectory is 10m . A large hoop is to be suspended from the celling by a massless cable at just the right place so that the clown will be able to dive through it when he reaches a maximum height above the ground. After passing through the hoop he will then continue on his trajectory until arriving at the safety net. Fig (2) shows a graph of the vertical component of the clown's velocity as a function of time between the cannon and the hoop. Since the velocity depends on the mass of the particular clown performing the act, the graph shows data for serveral different masses. If the angle the cannot makes with the horiaontal is increased from 45^(@) , the hoop will have to be