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.

Options

A. `(4500)/(sqrt(3))`
B. `(4500(sqrt(3)-1))/(sqrt(3))`
C. `4500sqrt(3)`
D. `(4500(sqrt(3)+1))/(sqrt(3))`

Answer

B

Explanation

`tan 60^(@)=(150)/(x)rArr x = (150)/(sqrt(3))`
Also, `tan 45^(@)=(150)/(x+y)`
`rArr x+y=150`
`rArr y=150-x=150-(150)/(sqrt(3))`
`rArr y=150((sqrt(3)-1)/(sqrt(3)))`= distance travelled
Speed (in m/hr) `=(150(sqrt(3)-1))/(sqrt(3))xx(60)/(2)=4500((sqrt(3)-1))/(sqrt(3))`