The driver of a matoroboat that can move at 10m/s in still water wishes to travel directly  across a river 1.6km wide in which the current flows at 5.0m/s. how long will it take to cross the river

To solve this problem, we need to determine the time it will take for the motorboat to travel directly across the river, given that the current flows perpendicular to the direction the driver wants to go.

### Given:
- Speed of the motorboat in still water: \( v_b = 10 \, \text{m/s} \)
- Speed of the current: \( v_c = 5 \, \text{m/s} \)
- Width of the river: \( d = 1.6 \, \text{km} = 1600 \, \text{m} \)

The boat is attempting to travel straight across the river. However, due to the current, the actual path will be diagonal. The key is to recognize that the time to cross the river depends only on the boat's speed in the direction perpendicular to the current (i.e., directly across the river).

The boat's speed across the river in the perpendicular direction remains \( v_b = 10 \, \text{m/s} \), as the current affects only the downstream motion.

### Time Calculation:
The time \( t \) to cross the river is calculated by dividing the distance by the boat's speed across the river:
\[
t = \frac{d}{v_b}
\]
\[
t = \frac{1600 \, \text{m}}{10 \, \text{m/s}} = 160 \, \text{seconds}
\]

### Answer:
The time it will take to cross the river is 160 seconds (or 2 minutes and 40 seconds).

Would you like more details or have any questions? Here are 5 related questions:

1. How can the current's speed impact the total distance traveled by the boat?
2. What would happen if the current speed increased to 7 m/s? How would that affect the time?
3. How would you calculate the boat’s actual diagonal path across the river?
4. What is the resultant velocity of the boat due to both its motion and the river current?
5. How would the crossing time change if the river were 2 km wide instead?

**Tip**: To find the resultant velocity when two vectors act at right angles (like the boat’s speed and the current), you can use the Pythagorean theorem.

The driver of a motorboat that can move at 10 m/s in still water wishes to travel directly across a river 1.6 km wide in which the current flows at 5.0 m/s. How long will it take to cross the river?

Discover how to calculate the time it takes for a motorboat moving at 10 m/s in still water to cross a river 1.6 km wide with a 5 m/s current. This kinematics problem involves using vector components and relative motion principles, suitable for Grades 9-12.

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