Advertisements
Advertisements
प्रश्न
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h.
उत्तर
Let the distance BC be x m and CD be y m.
In ΔABC
`tan 60^@ = (AB)/(BC) = 150/x`
`=> sqrt3 = 150/x`
`=> x = 150/sqrt3 m` ....(1)
In ΔABD
`tan 45^@ = (AB)/(BD) = 150/(x + y)`
`=> 1 = 150/(x + y)`
=> x + y = 150
`=> y = 150 - x`
Using 1 we get
`=> y = 150 - 150/sqrt3 = (150(sqrt3 - 1))/sqrt3 m`
Time taken to move from the point C to point D is 2 min = `2/60 h = 1/30 h`
Now.
Speed = `"Distance"/"Time" = y/(1/30)`
`=(150((sqrt3-1))/sqrt3)/(1/30) = 1500 sqrt3 (sqrt3 - 1) "m/h"`
APPEARS IN
संबंधित प्रश्न
The angle of depression of a car parked on the road from the top of a 150 m high tower is 30°. The distance of the car from the tower (in metres) is
`(A) 50sqrt3`
`(B) 150sqrt 3`
`(C) 150sqrt2`
`(D) 75`
The angle of elevation of the top of a tower as observed form a point in a horizontal plane through the foot of the tower is 32°. When the observer moves towards the tower a distance of 100 m, he finds the angle of elevation of the top to be 63°. Find the height of the tower and the distance of the first position from the tower. [Take tan 32° = 0.6248 and tan 63° = 1.9626]
There are two temples, one on each bank of a river, just opposite to each other. One temple is 50 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60° respectively. Find the width of the river and the height of the other temple.
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60° . At a point Y, 40m vertically above X, the angle of elevation is 45° . Find the height of tower PQ.
The angle of elevation of an aeroplane from a point on the ground is 45° after flying for 15seconds, the elevation changes to 30° . If the aeroplane is flying at a height of 2500 meters, find the speed of the areoplane.
An electrician has to repair an electric fault on a pole of height 4 meters. He needs to reach a point 1 meter 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?
Two ships are approaching a light-house from opposite directions. The angles of depression of the two ships from the top of the light-house are 30° and 45°. If the distance between the two ships is 100 m, find the height of the light-house. \[[Use \sqrt{3} = 1 . 732]\]
Two poles of heights 18 metre and 7 metre are erected on a ground. The length of the wire fastened at their tops in 22 metre. Find the angle made by the wire with the horizontal.
The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is `sqrt(st)`
The angle of elevation of the top of a 30 m high tower at a point 30 m away from the base of the tower is ______.
