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.
To find the time it takes for the boat to reach the opposite shore, we can break down the boat's motion into horizontal and vertical components.
First, we need to find the vertical component of the boat's velocity. Since the boat points upstream, we can consider the river's velocity as the negative y-component. Therefore, the vertical component of the boat's velocity is given by:
V_y = V_boat * sin(θ)
= 4.7 m/s * sin(24.4°)
≈ 2.02 m/s
Next, we need to find the horizontal component of the boat's velocity. The horizontal component of the boat's velocity remains unaffected by the river's flow. Therefore, the horizontal component of the boat's velocity is given by:
V_x = V_boat * cos(θ)
= 4.7 m/s * cos(24.4°)
≈ 4.27 m/s
Now, we can calculate the time it takes for the boat to cross the river. As the river is 25.9 m wide, the boat's displacement in the horizontal direction is 25.9 m. Using the horizontal component of the boat's velocity, we have:
d = V_x * t
25.9 m = 4.27 m/s * t
t ≈ 6.07 s
Therefore, it takes approximately 6.07 seconds for the boat to reach the opposite shore.