Answer:
a. Angle= 28.82°
b. Approved. He will get cold but he should be able to make it across
Explanation:
Velocity Vector
The velocity is a physical quantity that measures how fast or slow at a particular direction some object is moving. It must be expressed as a vector with both a magnitude and direction. If the object is confined to move in one direction, then we can use the speed as the scalar (magnitude only) equivalent of the velocity.
a.
The explorer wants to swim across a river to his campsite, as shown in the image below. The river has a velocity vr and the explorer can swim at ve in still water. If he swam directly to the campsite, he would end up in a point below it because the river would push him down. He must swim with a velocity such that he overcomes the stream but he advances to its objective. Let's call the angle he must swim at respect to the shoreline to achieve his goal. The explorer's velocity can be decomposed in its rectangular components vx and vy. To overcome the river's velocity:
[tex]v_{ey}=v_r[/tex]
We can compute the vertical component of the explorer's velocity as
[tex]v_{ey}=|v_e|cos\alpha[/tex]
Thus
[tex]v_r=|v_e|cos\alpha[/tex]
Solving for [tex]\alpha[/tex]
[tex]\displaystyle cos\alpha=\frac{v_r}{|v_e|}[/tex]
[tex]\displaystyle cos\alpha=\frac{0.665}{0.759}=0.876[/tex]
Then we have the angle is
[tex]\alpha=28.82^o[/tex]
b.
The horizontal component of the explorer's velocity is
[tex]v_{ex}=0.759sin28.82^o[/tex]
[tex]v_{ex}=0.366\ m/s[/tex]
This is the real velocity the explorer is having directly to the campsite
Knowing that
[tex]\displaystyle v=\frac{x}{t}[/tex]
Solving for t
[tex]\displaystyle t=\frac{x}{v}[/tex]
Calculating the time it takes the explorer to cross the river
[tex]\displaystyle t=\frac{29.3}{0.366}[/tex]
[tex]t=80\ sec[/tex]
Since this value is less than the limit value of hypothermia (300 sec), the decision is
Approved. He will get cold but he should be able to make it across
