A ferry can travel at an optimal speed of 8 km/h in still water measured relative to the shore. What is the optimal speed of the ferry, relative to the shore, if it moves perpendicular to a 6 km/h current?
A)4 km/h
B)8 km/h
C)10 km/h
D)14 km/h
E)28 km/h

Question

Quizplus · Accepted Answer

When the ferry moves perpendicular to the current, the speed of the ferry relative to the shore can be calculated using the Pythagorean theorem.

Let V be the velocity of the ferry relative to the shore and c be the speed of the current. Then, the speed of the ferry in the current is V + c in the direction parallel to the current and V - c in the direction perpendicular to the current.

Therefore, we have:

V^2 = (V + c)^2 + (V - c)^2
V^2 = 2V^2 + 2c^2
V^2 = c^2
V = c

Substituting the given values, we get:

V = 6 km/h + 8 km/h = 10 km/h

Hence, the optimal speed of the ferry, relative to the shore, if it moves perpendicular to a 6 km/h current, is 10 km/h.

A Ferry Can Travel at an Optimal Speed of 8