A boat crosses a river which is flowing at 6.0 m/s.The boat travels directly across the river from A to B and the speed of the boat relative to the river is 9.0 m/s.If it takes the boat 10.0 seconds to cross the river,how wide is the river?
A)108.1 m
B)89.2 m
C)67.1 m
D)60.0 m
E)150.0 m

Question

A boat crosses a river which is flowing at 6.0 m/s.The boat travels directly across the river from A to B and the speed of the boat relative to the river is 9.0 m/s.If it takes the boat 10.0 seconds to cross the river,how wide is the river? 
A)108.1 m 
B)89.2 m 
C)67.1 m 
D)60.0 m 
E)150.0 m

Quizplus · Accepted Answer

The boat travels directly across the river, which means that its path is a right angle to the direction of the river. We can draw a diagram to represent this:

B
     /    |
    /     |
   /      |
A/_______|

Let's call the width of the river "d". We know the speed of the river, "v_r", is 6.0 m/s and the speed of the boat relative to the river, "v_b", is 9.0 m/s.

Now we can use the formula:

d = v_r * t / sin(theta)

where "t" is the time it takes to cross the river and "theta" is the angle between the boat's path and the direction of the river. In this case, theta = 90 degrees, so sin(theta) = 1.

Plugging in the known values:

d = 6.0 m/s * 10.0 s / 1 
  = 60.0 m

Therefore, the width of the river is 60.0 m, which corresponds to answer choice C.

A Boat Crosses a River Which Is Flowing at 6