# The motor ship moves uniformly and in a straight line at a speed of 3 km / h relative to the water.

**The motor ship moves uniformly and in a straight line at a speed of 3 km / h relative to the water. A person walks along the deck at a speed of 4 km / h in a direction perpendicular to the speed vector of the motor ship. What is the speed of a person relative to water?**

Given:

v1 = 3 km / h – speed of the ship relative to the water;

v2 = 4 km / h – the speed of a person on the deck of the ship, perpendicular to the movement of the ship;

It is required to determine v (km / h) – the speed of a person’s movement relative to the water.

Since the speed of a person’s movement is directed perpendicular to the movement of the ship, then, according to the Pythagorean theorem:

v = (v1 ^ 2 + v2 ^ 2) ^ 0.5 = (3 ^ 2 + 4 ^ 2) ^ 0.5 = (9 + 16) ^ 0.5 = 25 ^ 0.5 = 5 km / h …

Answer: the speed of a person’s movement relative to the water is 5 kilometers per hour.