A camera operator is filming a nature explorer in the Rocky Mountains. The explorer needs to swim across a river to his campsite
. By watching debris flowing down the river, the operator estimates that the stream is flowing at
0.665
m
/
s
. In still water, the explorer can swim at
0.759
m
/
s
. At what angle, less than 90°, with respect to the shoreline should the operator advise him to swim so that he travels directly across the stream to his campfire?
angle:
°
The water is near freezing in temperature. Typically a human can only swim in such water for about
300
s
(or
5
min
) before hypothermia sets in. Calculate the time the explorer spends in the water if the river is
29.3
m
wide.
time in the water:
s
Based on the results, what should the camera operator's decision be about the explorer's swim?
Approved. He will get cold but he should be able to make it across.
Sorry, but the swim must be cancelled. He will never make it across in time.
0.665
m
/
s
. In still water, the explorer can swim at
0.759
m
/
s
. At what angle, less than 90°, with respect to the shoreline should the operator advise him to swim so that he travels directly across the stream to his campfire?
angle:
°
The water is near freezing in temperature. Typically a human can only swim in such water for about
300
s
(or
5
min
) before hypothermia sets in. Calculate the time the explorer spends in the water if the river is
29.3
m
wide.
time in the water:
s
Based on the results, what should the camera operator's decision be about the explorer's swim?
Approved. He will get cold but he should be able to make it across.
Sorry, but the swim must be cancelled. He will never make it across in time.
1 answer:
Answer:
a. Angle= 28.82°
b. Approved. Although he might feel cold, he should be able to cross.
Explanation:
Velocity Vector
Velocity is a measure of how quickly something is moving in a specific direction. It is represented as a vector that has both magnitude and direction. If an object can only move in one direction, then speed can serve as the scalar equivalent of that velocity (only focusing on magnitude).
a.
The explorer aims to swim across a river to reach his campsite, as depicted in the image below. The river's velocity is vr and the explorer's swimming speed in still water is ve. If he were to swim straight towards the campsite, he would end up downstream due to the river's current. Therefore, he must swim at an angle that allows him to overcome the current while still moving towards his goal. This angle relative to the shore is what we need to determine. The explorer's speed can be broken down into its horizontal (vx) and vertical (vy) components. In order to counteract the river's flow:
We can calculate the vertical component of the explorer's swimming speed as
Thus
Finding the value of
Then the angle is given by
b.
The component of the explorer's velocity that goes horizontally is
This represents the actual velocity directed towards the campsite
Considering that
To find t
Calculating the duration for the explorer to cross the river
As this time is under the hypothermia threshold (300 seconds), the conclusion is
Approved. Although he will feel cold, he should manage to cross successfully.
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Answer:
The duration, t = 3.53 seconds
Explanation:
The following information is provided:
The equation to calculate the time t is expressed as:
...... (1)
Where
s denotes the distance in feet
We are to determine the duration taken by the stone to fall a distance of 200 feet, where s = 200 feet
Substituting the value of s into equation (1) yields:
t = 3.53 seconds
Thus, the time taken by the object is 3.53 seconds, which provides the required answer.