a motorboat travels 25.0 km/h in still water. what will be the magnitude and direction of the velocity of the boat if it is directed upstream on a river that flows at the rate of 4.00 km/h?

Since it is going upstream, subtract the river flow velocity.

A river flows at a uniform speed of 2ms-1 and is 100m wide. A motor boat

has a maximum speed in still water of 7ms-1

To determine the magnitude and direction of the velocity of the boat when it's traveling upstream on a river, we need to take into account the velocities of the boat and the river.

Given:
- The speed of the motorboat in still water (relative to land) is 25.0 km/h.
- The speed of the river flow is 4.00 km/h.

When the boat is traveling upstream, it moves against the current of the river. This means we need to subtract the speed of the river from the speed of the boat to get the resultant velocity.

To find the magnitude of the velocity:
Magnitude = Boat speed - River speed
Magnitude = 25.0 km/h - 4.00 km/h
Magnitude = 21.0 km/h

So, the magnitude of the boat's velocity when traveling upstream is 21.0 km/h.

To find the direction of the velocity:
The direction will be opposite to the direction of the river flow because the boat is moving upstream against the current.

Therefore, the direction of the boat's velocity is upstream.

In summary, the magnitude of the boat's velocity when traveling upstream is 21.0 km/h, and the direction is upstream.

To find the magnitude and direction of the velocity of the boat when it is directed upstream on a river, you need to consider the relative motion between the boat and the river.

Let's break down the problem step by step:

1. The boat's speed in still water is given as 25.0 km/h. This means that if there were no current, the boat would travel at a speed of 25.0 km/h.

2. The river flows at a rate of 4.00 km/h. This means that the current is acting in the opposite direction to the boat's motion.

3. When the boat travels upstream, the effective speed is the difference between the boat's speed in still water and the speed of the current. So, the effective speed will be 25.0 km/h - 4.00 km/h = 21.0 km/h.

4. The magnitude of the velocity of the boat will be the effective speed, which is 21.0 km/h.

5. To determine the direction, you need to consider the boat's motion relative to the river. Since the river is flowing in the opposite direction to the boat's motion, the direction of the boat's velocity will be upstream, against the direction of the current.

So, the magnitude of the velocity of the boat when it is directed upstream on the river will be 21.0 km/h, and the direction will be upstream.