A swimmer is capable of swimming 0.45 m/s in still water.

(a) If she aims her body directly across a 75 m-wide river whose current is 0.30 m/s, how far downstream (from a point opposite her starting point) will she land?
(b) How long will it take her to reach the other side?

Help is desperately needed. Ive been sick and missed school for 4 days and my teacher is still making the assignment due for me the same day as everyone else!

How long does it take to swim 75m at.45m/s? Take that time, and find the distance he was swept downstream(.45*time).

I'm sorry to hear that you've been sick and missed school. Don't worry, I'm here to help you with your assignment. Let's break down the problem step by step.

(a) To find how far downstream the swimmer will land, we can use the concept of relative velocity.

Relative velocity of the swimmer with respect to the ground is the vector subtraction of the swimmer's velocity and the river's velocity.

Given:
Swimmer's velocity in still water = 0.45 m/s
River's current velocity = 0.30 m/s
Width of the river = 75 m

To find the distance downstream, we can use the formula: distance = speed × time.

The time taken to cross the river is the same as the time taken to travel the width of the river:

Time = Distance / Relative velocity

Relative velocity = Swim velocity - River velocity
Relative velocity = 0.45 m/s - 0.30 m/s = 0.15 m/s

So, Time = 75 m / 0.15 m/s = 500 seconds

Therefore, the swimmer will land 500 seconds downstream from her starting point.

(b) To find how long it will take her to reach the other side, we can use the concept of the Pythagorean theorem.

The speed of the swimmer relative to the ground can be found using the Pythagorean theorem:

Relative speed = √((Swim velocity)^2 + (River velocity)^2)

Relative speed = √((0.45 m/s)^2 + (0.30 m/s)^2) = √(0.2025 m^2/s^2 + 0.09 m^2/s^2) = √0.2925 m^2/s^2 = 0.54 m/s

Now, we can use the formula: time = distance / speed.

The distance to be traveled is the width of the river, which is 75 meters.

Therefore, Time = 75 m / 0.54 m/s = 138.89 seconds (rounded to two decimal places).

So, it will take the swimmer approximately 138.89 seconds to reach the other side of the river.

Please note that these calculations are based on the given information, and if you have any additional information or assumptions, please let me know so that I can adjust the steps accordingly.

I'm sorry to hear that you've been sick. I'll do my best to help you with this problem.

To solve this question, we need to consider the swimmer's velocity and the velocity of the river current.

(a) To determine the distance downstream where she will land, we need to calculate the vector sum of the swimmer's velocity and the river's current. We can use the concept of relative motion to find the resultant velocity.

Let's break the velocities into horizontal and vertical components. The swimmer's velocity in still water (0.45 m/s) is only along the horizontal direction since there is no vertical component mentioned.

The swimmer's velocity can be represented as:
Swimmer's velocity = 0.45 m/s (horizontal component) + 0 m/s (vertical component).

Similarly, the river's current can be represented as:
River's current velocity = 0.30 m/s (horizontal component) + 0 m/s (vertical component).

To find the resultant velocity, we need to add the horizontal components and vertical components separately.

Horizontal component of resultant velocity = swimmer's velocity - river's current velocity
= 0.45 m/s - 0.30 m/s
= 0.15 m/s.

Vertical component of resultant velocity = 0 m/s - 0 m/s = 0 m/s. (Since both the swimmer's velocity and the river's current do not have vertical components)

Now, we have the resultant velocity as 0.15 m/s (horizontal component) and 0 m/s (vertical component).

To calculate the distance downstream the swimmer will land, we can use the formula:

Distance = resultant velocity × time.

The time taken will be the time needed to cross the river, which we will find in part (b).

(b) To find the time taken to reach the other side, we can use the formula:

Time = distance / velocity.

The distance is given as 75 m (width of the river) and the velocity is the horizontal component of the resultant velocity, which we calculated in part (a) as 0.15 m/s.

Now we can calculate the time it will take the swimmer to reach the other side using the formula mentioned above.

Please input the following calculations and the answers should be obtained:

(a) Distance downstream (from a point opposite her starting point) = horizontal component of resultant velocity × time.

(b) Time taken to reach the other side = distance / velocity.

I hope this explanation helps you to understand the problem and solve it successfully. Let me know if you have any further questions!