A harbour lies in a direction `60^@` south - west from a fort and at a distance 30 km from it .A ship sets from the habour at noon and sails due east at 10 km / hour .The ship will be 70 km from the fort at

Options

A. 7 p.m
B. 8 p.m
C. 5 p.m
D. 10 p.m

Explanation

Let A be the position of the harbour and O be the fort . OA =30 OB=70. Let AB=x

Applying cosine formula in `DeltaOAB` , we get
`cos60^@= (OA^2+AB^2-OB^2)/(2OA.AB)`
`rArr 1/2= (900+x^2-4900)/(2xx30xxx)`
`rArr x^2-30x-4000=0`
`rArr x=80`
AB= 80 km
Speed of ship = ` 10 km // hr `
`therefore Time = 8 hr `