Relative motion question again

[F.B]

I really need help with this question

A swimmer who achieves a speed of 0.75 m/s in still water swims directly across a river 72 m wide. The swimmer lands on the far shore at a position 54 m down stream from the starting point.
a)Determine the speed of the river current.
b)Determine the swimmer's velocity relative to the shore.
c)Determine the direction the swimmer would have to aim to land directly across from the starting position.

I did (a) and (b).
For (a) i got 0.5 m/s
For (b) i got 0.94 m/s

I have no idea what so ever how to do (c). Can anyone please atleast help me with this one??

 

[physumr]

Make this problem into a triangle and try inverting the angle.

 

[quicknote]

First of all, I would recommend using a diagram to visualize the situation. Draw a river with a width of 72 m and label the starting point and the landing point. Then draw a line connecting the two points to represent the swimmer's path.

To determine the direction the swimmer would have to aim, we need to consider the relative motion of the swimmer and the river current. Since the swimmer is moving at a velocity of 0.75 m/s in still water, we can say that their velocity relative to the shore is also 0.75 m/s.

However, the river current is also moving at a velocity of 0.5 m/s. This means that the swimmer's actual velocity relative to the shore is 0.75 m/s - 0.5 m/s = 0.25 m/s.

To land directly across from the starting position, the swimmer would have to aim in a direction that compensates for the river current. In other words, the swimmer would have to aim slightly upstream in order to counteract the downstream motion caused by the current.

To determine the exact angle, we can use trigonometry. Since we know the width of the river (72 m) and the distance downstream (54 m), we can use the tangent function to calculate the angle.

tan θ = opposite/adjacent = 54/72
θ = tan^-1(54/72)
θ = 37.4 degrees

Therefore, the swimmer would have to aim at an angle of 37.4 degrees upstream in order to land directly across from the starting position.

I hope this helps! Remember to always draw a diagram and break down the problem into smaller, more manageable parts. Good luck!