Question

[URGENT] A swimmer wants to end up at a dock due north of her starting position on the south shore of a river. In still water her maximum speed is 1.25m/s. The river has a current flowing 0.35m/s [E].

a.) calculate the direction that she must aim herself through the water to arrive at the dock.

b.) how long will it take for the swimmer to cross the river, if the distance from the starting point to the dock is 300 m?

Please show all your work, thanks

Answer 1

Explanation:

As you can see in the picture, we want the swimmer to go on a straight line, so the speed of the water must be equal to the speed of the swimmer along the x-axis. We also know the value of v, so we can calculate the of the cosine of the angle (alpha) between Vx and V. Thanks to the fundamental relation of gioniometry (cos^2(x) + sin^2(x) = 1) we can find the sine of alpha and calculate Vy. With Vy we can calculate the time that the swimmer will use for reaching the dock: s = Vy * t => t = s/(Vy).

I'll let you do all the calculations, you just have to plug in values.

Answer 2

a)The direction that she must aim herself through the water to arrive at the dock will be 73.7°.

b)The time it takes for the swimmer to cross the river will be 240 seconds.

What is speed?

Speed is defined as the rate of change of the distance or the height attained. it is a time-based quantity. it is denoted by u for the initial speed while v for the final speed. its si unit is m/sec.

Given data;

The maximum speed of the swimmer In still water,v=1.25m/s.

Speed of river = 0.35m/s [E]

α is the direction that she must aim herself through the water to arrive at the dock.

t is the time it takes for the swimmer to cross the river

The distance from the starting point to the dock is,s = 300 m

If the swimmer were to swim straight, the water's speed along the x-axis would have to match that of the swimmer.

$\rm v_w = v_x = 0.35 \ m/sec$

α is the angle between vx and v

The value of the

$\rm cos \alpha = \frac{v_x}{v} \\\\ \alpha = cos ^{-1}(\frac{0.35}{1.25} )\\\\ \alpha = 73.7 ^0$

The time that the swimmer will use for reaching the dock;

s = V×t

t = s/(v)

t=300 m / 1.25 m/sec

t = 240 seconds

Hence, the direction that she must aim herself through the water to arrive at the dock. and it takes for the swimmer to cross the river will be 73.7° and 240 seconds respectively.

To learn more about the speed refer to the link;

https://brainly.com/question/7359669

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