A harbour lies in the direction 60 o south-west from a fort and at a distance of 30 km from it. A ship sets out from the harbour at noon and sails due east at 10 km/hour, then the time (in hours) in the evening at which the ship will be 70 km from the fort is

Step-by-step solution

Let A be the position of the harbour and O be of the fort. O A   = 30 ,   O B = 70 . Let A B =   x . Applying cosine formula in Δ O A B , we get cos 60 o = O A 2 + A B 2 − O B 2 2 O A . A B ⇒ 1 2 = 900 + x 2 − 4900 2 × 30 × x ⇒ x 2 − 30 x − 4000 = 0 ⇒ x = 80 A B = 80 kms Speed of ship = 10 km/hr ∴ Time = 8 hrs