Sheena can row a boat at 2.91 mi/h in still water. She needs to cross a river that is 1.24 mi wide with a current flowing at 1.54 mi/h. Not having her calculator ready, she guesses that to go straight across, she should head 60.0° upstream.

(a) What is her speed with respect to the starting point on the bank?

(b) How long does it take her to cross the river?

(c) How far upstream or downstream from her starting point will she reach the opposite bank?
magnitude
direction

(d) In order to go straight across, what angle upstream should she have headed????

Please helppp

To solve this problem, we need to break down the different components and apply the principles of vector addition.

(a) To find Sheena's speed with respect to the starting point on the bank, we can break down her velocity into a horizontal component parallel to the bank and a vertical component perpendicular to the bank.

The horizontal component of her velocity will be her speed in still water multiplied by the cosine of the angle she is heading relative to the bank. Given that Sheena's speed in still water is 2.91 mi/h and she is heading 60.0° upstream, the horizontal component of her velocity can be calculated as follows:

Horizontal component = 2.91 mi/h * cos(60.0°)

(b) To determine how long it takes Sheena to cross the river, we need to calculate the time it takes for her to travel the horizontal distance.

Time = Distance / Horizontal component

Given that the river width is 1.24 mi, we can substitute the calculated horizontal component from part (a) into the equation to find the time.

(c) To determine how far upstream or downstream from her starting point she will reach the opposite bank, we need to calculate the vertical component of her velocity.

The vertical component of her velocity will be her speed in still water multiplied by the sine of the angle she is heading relative to the bank. Given that Sheena's speed in still water is 2.91 mi/h and she is heading 60.0° upstream, the vertical component of her velocity can be calculated as follows:

Vertical component = 2.91 mi/h * sin(60.0°)

Now, we can calculate the distance by multiplying the time from part (b) with the vertical component of her velocity:

Distance = Time * Vertical component

(d) Finally, to determine the angle Sheena should have aimed to go straight across the river, we can use the concept of vector addition.

The resultant velocity vector (straight across the river) is the vector sum of the velocity of Sheena and the velocity of the current. If Sheena aims straight across the river, the resultant velocity vector should be perpendicular to the bank. To find the angle, we can use trigonometry and calculate the inverse tangent of the vertical component of the velocity divided by the horizontal component of the velocity.

Angle upstream = atan(Vertical component / Horizontal component)

Now, by following these steps, we can find the answers to each of the questions.