Question

A man in a boat rowing away from a light house 100m high takes 2min to change the angle of elevation of the top of the light house from 60degree to 30degree . Find the speed of the boat in meters per min . Use {3 = 1.732}

Answer 1

Answer:

0.35219 m/s

Explanation:

Step-by-step explanation:

Height of the Light house , p = 100 m

let initial distance be x m

and the angle is 60°

so, tan60° = p/x = 100/x

or, √3 = 100/x

or, x = 100/√3 m

Now after time 2min let the new distance be y

and angle is 45°

so, tan45° = 100/y

so, 1 = 100/y

so, y = 100 m

So, distance travelled in 2min

= y - x = 100 - 100/√3 = 100 - 57.737

= 42.263 m

So, d = 42.263 m

t = 2 min = 2×60 = 120 sec

speed = d/t = 42.263/120 m/s

= 0.35219 m/s

Going away from the light house with a speed of 0.35219 m/s.