You are riding in a boat whose speed relative to the water is 6.9 m/s. The boat points at an angle of 25.0° upstream on a river flowing at 15.1 m/s. Find the time it takes for the boat to reach the opposite shore if the river is 26.5 m wide.
It does not matter how fast the water is flowing. That just affects where on the opposite side you wind up.
Since the boat is moving at an angle of 25.0° upstream, the distance traveled is given by
26.5/d = cos 25.0°
divide the distance by the speed to get the travel time:
t = d/s = (26.5/cos25.0°)/6.9 = 4.23 s
Q: what the heck puny river is only 26.5m wide? That's barely a crick!
To find the time it takes for the boat to reach the opposite shore, we need to first break down the boat's velocity into its horizontal and vertical components.
Let's start by finding the horizontal component of the boat's velocity. The boat's speed relative to the water is given as 6.9 m/s, and it points at an angle of 25.0° upstream, which means we need to find the component of the boat's velocity in the downstream direction.
Using trigonometry, we can determine the horizontal component of the boat's velocity using the given angle. The horizontal component (Vh) can be found using the formula: Vh = V * cos(θ), where V is the boat's speed relative to the water and θ is the angle relative to the downstream direction.
Vh = 6.9 m/s * cos(25.0°) = 6.9 m/s * 0.9063 ≈ 6.26 m/s
Now, let's find the river's velocity. The river is flowing at a speed of 15.1 m/s. Since the boat is moving upstream, we need to subtract the river's velocity from the boat's velocity to determine the effective velocity of the boat in the upstream direction.
Vupstream = Vh - Vriver = 6.26 m/s - 15.1 m/s ≈ -8.84 m/s
Note that the negative sign indicates that the boat is moving against the river's flow.
Next, we can find the time it takes for the boat to cross the river. The river's width is given as 26.5 m.
We can use the formula: time = distance / velocity. In this case, the distance is the width of the river and the velocity is the effective velocity of the boat in the upstream direction.
Time = 26.5 m / 8.84 m/s ≈ 2.99 s
Therefore, it takes approximately 2.99 seconds for the boat to reach the opposite shore.