You are riding in a boat whose speed relative to the water is 4.7 m/s. The boat points at an angle of 24.4° upstream on a river flowing at 13.1 m/s. Find the time it takes for the boat to reach the opposite shore if the river is 25.9 m wide.
the cross-stream speed is 4.7 cos 24.4° = 4.29m/s
So, it takes 25.9/4.29 = 6.04 sec
The speed of the river does not matter, unless you want to find how far upstream or downstream the boat lands.
To find the time it takes for the boat to reach the opposite shore, we need to break down the motion of the boat into its horizontal and vertical components.
First, let's find the horizontal component of the boat's velocity. Since the boat is pointing upstream, its horizontal velocity will be affected by the river's flow. We can use trigonometry to find this component:
horizontal velocity = boat speed x cosine(angle)
horizontal velocity = 4.7 m/s x cos(24.4°)
Next, we can find the vertical component of the boat's velocity. Since the boat is traveling perpendicular to the river's flow, the vertical velocity is unaffected by the river:
vertical velocity = boat speed x sine(angle)
vertical velocity = 4.7 m/s x sin(24.4°)
Now, let's consider the motion of the boat in the horizontal direction. The boat needs to travel a distance of 25.9 m to reach the opposite shore. We can use the formula:
distance = speed x time
Substituting the values we have:
25.9 m = horizontal velocity x time
We can rearrange this equation to solve for time:
time = distance / horizontal velocity
time = 25.9 m / (4.7 m/s x cos(24.4°))
Now we can plug in the values and calculate the time it takes for the boat to reach the opposite shore.