A sail boat is crossing a river of width 43.3 meters, sailing at 17.9 m/s vertically across the river. If a cross wind of 6.0 m/s directed 19.6 degrees off of vertical pushes the sailboat, then how far downstream (horizontally) will the boat be when it reaches the other side of the river? (please provide your answer to 1 decimal place)

Question

A sail boat is crossing a river of width 43.3 meters, sailing at 17.9 m/s vertically across the river. If a cross wind of 6.0 m/s directed 19.6 degrees off of vertical pushes the sailboat, then how far downstream (horizontally) will the boat be when it reaches the other side of the river? (please provide your answer to 1 decimal place)

Answer 1

We can use trigonometry to solve this problem.

First, we can find the velocity of the sailboat in the horizontal direction (downstream) using the cross wind:

V_horizontal = V_wind * cos(angle_off_vertical) = 6.0 m/s * cos(19.6 degrees) = 5.697 m/s

Next, we can use the Pythagorean theorem to find the total speed of the sailboat:

V_total = sqrt((V_sailboat)^2 + (V_horizontal)^2) = sqrt((17.9 m/s)^2 + (5.697 m/s)^2) = 18.771 m/s

Finally, we can use the formula distance = speed * time to find how far downstream the sailboat will be after crossing the river. The time it takes to cross the river can be found using the width of the river and the vertical speed of the sailboat:

time = distance_vertical / V_sailboat = 43.3 m / 17.9 m/s = 2.42 s

Then, the distance downstream can be found using:

distance_downstream = V_horizontal * time = 5.697 m/s * 2.42 s = 13.8 meters

Therefore, the sailboat will be 13.8 meters downstream (horizontally) when it reaches the other side of the river.