What is the correct calculation for the speed of a boat heading across a river flowing at 4m/s with a speed of 3m/s?

The calculation for the speed of a boat moving across a river while also considering the river's current requires the use of the Pythagorean theorem. In this scenario, we have two velocity components: one for the boat's speed across the river (3 m/s) and another for the river's current flowing downstream (4 m/s).

Since these two speeds are perpendicular to each other—one is directed across the river and the other downstream—we cannot simply add their magnitudes together; instead, we need to apply vector addition. The resultant speed of the boat is found by calculating the magnitude of the resultant vector formed by these two perpendicular components.

According to the Pythagorean theorem, the magnitude of the resultant velocity ( v ) can be determined using the formula:

[ v = \sqrt{(v_{boat})^2 + (v_{river})^2} ]

Inserting the values gives:

[ v = \sqrt{(3,m/s)^2 + (4,m/s)^2} ] [ v = \sqrt{9 + 16} ] [ v = \sqrt{25} ] [ v = 5,m/s ]

This demonstrates that when you have