1

Question

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform speed. At that point, angle of depression of the boat with the man’s eye is 30∘ (Ignore man’s height). After sailing for 20 seconds, towards the base of the tower (which is at the level of water), the boat has reached a point B, where the angle of depression is 45∘. Then the time taken (in seconds) by the boat from B to reach the base of the tower is :

Open in App

Solution

The correct option is **D** 10(√3+1)

hx+y=tan30∘

x+y=√3h ....(1)

also

hy=tan45∘

h=y ...(2)

put h=y in equation (1)

x+y=√3y

x=(√3−1)y

and

x20= ′v ′ (v= speed)

∴ time taken to reach foot from B

=yv

=x(√3−1)×x×20

=10(√3+1)

hx+y=tan30∘

x+y=√3h ....(1)

also

hy=tan45∘

h=y ...(2)

put h=y in equation (1)

x+y=√3y

x=(√3−1)y

and

x20= ′v ′ (v= speed)

∴ time taken to reach foot from B

=yv

=x(√3−1)×x×20

=10(√3+1)

0

View More

Join BYJU'S Learning Program

Join BYJU'S Learning Program