You are riding in a boat whose speed relative to the water is 7.4 m/s. The boat points at an angle of 24.8° upstream on a river flowing at 15.2 m/s. Find the time it takes for the boat to reach the opposite shore if the river is 26.1 m wide.

speed across = 7.4 cos 24.8

time = distance/speed
= 26.1 / 7.4 cos 24.8

the river speed only says how far downstream he will end up.

To solve this problem, we can split the motion into horizontal and vertical components. Let's consider the horizontal component first.

The boat is pointing upstream at an angle of 24.8°. This means that the horizontal component of the boat's velocity is given by:

Vx = 7.4 m/s * cos(24.8°).

Now, let's consider the vertical component of motion. The boat is not moving vertically relative to the water, so the velocity in the y-direction is zero.

Next, let's examine the river's velocity. The river is flowing downstream at a speed of 15.2 m/s. Since the boat is pointing upstream, the effective velocity of the river in the x-direction is given by:

Vy_river = 15.2 m/s * cos(180° - 24.8°).

Now we can find the total velocity of the boat relative to the shore. The x-component of the boat's velocity is the difference between the boat's velocity relative to the water and the velocity of the river:

Vx_total = Vx - Vy_river.

The time taken for the boat to reach the opposite shore can be determined by dividing the distance it needs to cross (26.1 m) by the total velocity of the boat in the x-direction:

Time = Distance / Vx_total.

By substituting the given values and solving this equation, we can find the time it takes for the boat to reach the opposite shore.