A boat attempts to cross a 172 m wide river to reach a dock directly on the other side. The boat heads out directly across the river, perpendicular to the bank, with the motor propelling it at 16 m/s across the water, but he river flowing at 5.4 m/s immediately begins pushing it down river. How far down river ( in meters) from the dock does the boat end up when it reaches the opposite shore?
To determine how far down the river the boat ends up when it reaches the opposite shore, we can use the concept of vectors. We'll break down the motion of the boat into its horizontal and vertical components.
Let's first find the time it takes for the boat to cross the river. We can use the equation:
time = distance / speed
The distance the boat needs to cross is the width of the river, which is 172 m. The speed of the boat across the water is 16 m/s. Therefore,
time = 172 m / 16 m/s
time ≈ 10.75 s
Now, let's determine how far downstream the river flows during this time. We can use the equation:
distance downstream = speed downstream x time
The speed downstream is the velocity of the river, which is given as 5.4 m/s. The time is 10.75 s (as calculated previously). Therefore,
distance downstream = 5.4 m/s x 10.75 s
distance downstream ≈ 58.05 m
Hence, when the boat reaches the opposite shore, it will be approximately 58.05 meters downstream from the dock.