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)

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 need to find the horizontal component of the boat's velocity. This is given by:

horizontal velocity = sailboat speed x cos(wind angle)

horizontal velocity = 17.9 m/s x cos(19.6°)

horizontal velocity = 16.9 m/s

Next, we need to find how long it takes for the boat to cross the river. This is given by:

time to cross = distance / vertical velocity

time to cross = 43.3 m / 17.9 m/s

time to cross = 2.42 s

Finally, we can find how far downstream the boat will be at the end of this time. This is given by:

downstream distance = time to cross x horizontal velocity

downstream distance = 2.42 s x 16.9 m/s

downstream distance = 40.9 m

Therefore, the sailboat will be approximately 40.9 meters downstream when it reaches the other side of the river.