River Boat Problems

Your motor propels your boat across a 20 m wide river (with a current of 6 m/s S) at a rate of 10 m/s.

In the diagram to the right - which leg of the triangle should be 10 m/s?

• Green

• Red

• Blue

• Not Depicted

Answer explanation

Your speed is always the direction YOU choose to go. The resulting velocity only occurs because the river is also acting on you.

Tags

NGSS.HS-PS2-1

Your motor propels your boat across a 20 m wide river (with a current of 6 m/s S) at a rate of 10 m/s.

Which two quantities should you use to calculate how long it takes to cross the river?

• distance of 20 m & speed of 6 m/s

• distance of 20 m & speed of 11.7 m/s

• distance of 20 m & speed of 10 m/s

• Not enough information to determine.

Answer explanation

The boat's horizontal velocity dictates how much time it should take to travel a horizontal distance.

Your motor propels your boat across a 20 m wide river (with a current of 6 m/s S) at a rate of 10 m/s.

How long does it take you to cross the river?

• 2 seconds

• 200 seconds

• 3.33 seconds

• Not enough information to determine.

Answer explanation

The boat's horizontal velocity dictates how much time it should take to travel a horizontal distance.

Your motor propels your boat across a 20 m wide river (with a current of 6 m/s S) at a rate of 10 m/s.

If it takes you two seconds to cross the river, how far down stream will you come ashore?

• 12 m

• 20 m

• 22.2 m

• Not enough information to determine.

Answer explanation

As you are moving across the river the current pulls you down stream at a rate of 6 m every second. If it takes you 2 seconds to cross, then you will have moved 12 m down stream.

The image to the right organizes the velocity and displacement information from a riverboat word problem into two triangles.

*Assume the boat is crossing a south flowing stream towards the eastern shore.

What is the strength of the current?

• 24 m/s

• 6 m/s

• 8 m/s

• 10 m/s

Answer explanation

The flow rate of the stream will be shown in the velocity diagram.

Because the stream flows south - the vertical leg of the right triangle would be its rate.

The image to the right organizes the velocity and displacement information from a riverboat word problem into two triangles.

*Assume the boat is crossing a south flowing stream towards the eastern shore.

What is the speed of the boat?

• 24 m/s

• 6 m/s

• 8 m/s

• 10 m/s

Answer explanation

The speed of the boat will be shown in the velocity diagram.

Because the boat is traveling to the eastern shore - the horizontal leg of the right triangle would be its rate.

The image to the right organizes the velocity and displacement information from a riverboat word problem into two triangles.

*Assume the boat is crossing a south flowing stream towards the eastern shore.

What is the magnitude of the resultant velocity of the boat?

• 14 m/s

• 6 m/s

• 8 m/s

• 10 m/s

Answer explanation

The resultant velocity is the "total" velocity of the boat accounting for both the motor and the current.

Adding these two together (using trig) yields length of the hypotenuse.

The image to the right organizes the velocity and displacement information from a riverboat word problem into two triangles.

*Assume the boat is crossing a south flowing stream towards the eastern shore.

What does the "24" represent?

• The width of the river.

• The overall displacement of the boat.

• The distance downstream the boat travels.

• Not enough information to determine.

Answer explanation

The vertical leg of the displacement triangle would be the "vertical" displacement. In this case the river flows south so it would be distance downstream the boat is carried.

The image to the right organizes the velocity and displacement information from a riverboat word problem into two triangles.

*Assume the boat is crossing a south flowing stream towards the eastern shore.

How wide is the river?

• 24 m

• 6 m

• 18 m

• Not enough information to determine.

Answer explanation

The horizontal leg of the displacement triangle would be the "horizontal" displacement. In this case the river flows south so the width of the stream would be the horizontal leg.

The simpleist way to calculate this would be to use the fact that they are similar triangles.

The image to the right organizes the velocity and displacement information from a riverboat word problem into two triangles.

*Assume the boat is crossing a south flowing stream towards the eastern shore.

How long does it take the boat to cross?

• 3 seconds

• 4 seconds

• 4.5 seconds

• Not enough information to determine.

Answer explanation

Use the distance downstream and the velocity downstream to calculate time.

d=vt

24=8t