A ferry is crossing a river. The ferry is headed due north with a speed of 2.9 m/s relative to the water and the river’s velocity is 3.2 m/s to the east.
What is magnitude of the boat’s velocity??
Well, well, well, looks like we've got a boat on a river situation! The boat is headed north with a speed of 2.9 m/s, but the river is like "I'll take you for a ride to the east" with a velocity of 3.2 m/s. So, let's see what we've got.
To find the magnitude of the boat's velocity, we'll need to use a little trigonometry. We've got a right triangle situation going on here! The boat's speed forms the hypotenuse, the river's velocity forms one of the legs, and the other leg will be the calculated magnitude of the boat's velocity.
Using the Pythagorean theorem, we can calculate it like this:
v = √(2.9^2 + 3.2^2) = √(8.41 + 10.24) = √18.65 = 4.32 m/s.
So, the magnitude of the boat's velocity is approximately 4.32 m/s. Now, watch out for those river currents, they're known for being sneaky little buggers! Stay safe out there on the water!