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 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.

Answer 2

To find the distance downstream that the sailboat will be when it reaches the other side of the river, we can use trigonometry.

Let's denote the vertical component of the boat's velocity as Vy, the horizontal component of the boat's velocity as Vx, and the time it takes for the boat to cross the river as t.

The vertical component of the boat's velocity can be calculated using the sailboat's speed and the angle of the crosswind:

Vy = speed * sin(angle)
= 17.9 m/s * sin(19.6 degrees)
≈ 6.2 m/s

The horizontal component of the boat's velocity is equal to the crosswind's velocity:

Vx = crosswind velocity
= 6.0 m/s

Now, we can determine the time it takes for the boat to cross the river using the width of the river and the horizontal component of the boat's velocity:

t = width / Vx
= 43.3 m / 6.0 m/s
≈ 7.2 s

Finally, we can find the distance downstream that the boat will be when it reaches the other side by multiplying the time it takes to cross with the vertical component of the boat's velocity:

Distance downstream = Vy * t
= 6.2 m/s * 7.2 s
≈ 44.6 m (to 1 decimal place)

Therefore, the boat will be approximately 44.6 meters downstream when it reaches the other side of the river.