A swimmer swam north at 1.75 m/s across a current running from west to east at 2 m/s. She swam for 20 s. How far did she travel, rounded to the nearest tenth of a metre?
A) 75 m
B) 53.2 m
C) 2.7 m
D) 26.6 m
did you make a sketch?
I had x^2 = (20(1.75))^2 + (20(2))^2 =2825
x =√2825 = appr 53.2
To find the distance the swimmer traveled, we need to calculate her net displacement.
The swimmer swam north at a speed of 1.75 m/s for 20 seconds, which gives a displacement of 1.75 m/s * 20 s = 35 meters north.
The current is running from west to east at a speed of 2 m/s. Since the swimmer is swimming north and the current is running perpendicular, it does not affect the swimmer's northward displacement.
Therefore, the swimmer traveled a total distance of 35 meters, rounded to the nearest tenth of a meter.
The correct answer is A) 35 meters.
To determine the distance the swimmer traveled, we need to consider both the swimmer's speed and the effect of the current.
First, let's break down the swimmer's movement into the vertical (north-south) and horizontal (east-west) components. We are given that the swimmer's speed, relative to the water, is 1.75 m/s to the north. Since the swimmer is only swimming on the north-south axis, we can say that her velocity in the east-west direction (horizontal component) is zero.
Now, let's consider the effect of the current. The current is flowing from west to east at a speed of 2 m/s. Since the swimmer is swimming perpendicular to the current, the current does not directly affect her north-south velocity. However, the current does affect her east-west velocity.
To find the relative velocity, we can subtract the current speed from the swimmer's speed. In this case, the swimmer's east-west velocity is 0 m/s (from swimming directly north) minus 2 m/s (from the current), giving us a relative velocity of -2 m/s in the east-west direction. The negative sign indicates that the swimmer is moving in the opposite direction of the current.
To find the total distance the swimmer traveled, we can use the formula:
Distance = (speed)(time)
Since we are working with a vector quantity (distance), we need to remember to account for both the north-south and east-west components separately.
First, let's find the distance traveled in the north-south direction:
Distance north-south = (north-south velocity)(time)
Distance north-south = (1.75 m/s)(20 s)
Distance north-south = 35 m
Next, let's find the distance traveled in the east-west direction:
Distance east-west = (east-west velocity)(time)
Distance east-west = (-2 m/s)(20 s)
Distance east-west = -40 m
Since distance cannot be negative, we can take the absolute value of the east-west distance to find the magnitude:
|Distance east-west| = 40 m
To determine the total distance traveled, we can use the Pythagorean theorem to calculate the magnitude of the distance vector:
Distance = √(Distance north-south)^2 + (Distance east-west)^2
Distance = √((35 m)^2 + (40 m)^2)
Distance ≈ 53.2 m
Therefore, the swimmer traveled approximately 53.2 m, rounded to the nearest tenth of a meter.
Therefore, the answer is (B) 53.2 m.