Answer:
The velocity component in south direction is 42.42 miles/hour and in west direction is 42.42 miles/hour.
Explanation:
Given that,
Speed = 60 miles/hour
Direction = south west
Let the south in y axis and west in x axis.
Angle between x and y will be θ.
The component of speed is [tex]V_{x}[/tex] of x axis and [tex]V_{y}[/tex] of y axis.
[tex]\vect{V}=\vec{V_{x}i}+\vec{V_{y}j}[/tex]
Where,
[tex]V_{x}=|\vec{V}|\cos\theta[/tex]...(I)
[tex]V_{y}=|\vec{V}|\sin\theta[/tex]....(II)
We know that,
The south west direction makes 45° with west direction in x axis.
(a). We need to calculate the velocity component in south direction
Using equation (I)
[tex]V_{x}=|\vec{V}|\cos\theta[/tex]
Put the value into the formula
[tex]V_{x}=60\times\cos45[/tex]
[tex]V_{x}=42.42\ miles/hour[/tex]
(b). We need to calculate the velocity component in west direction
Using equation (II)
[tex]V_{x}=|\vec{V}|\sin\theta[/tex]
Put the value into the formula
[tex]V_{x}=60\times\sin45[/tex]
[tex]V_{x}=42.42\ miles/hour[/tex]
Hence, The velocity component in south direction is 42.42 miles/hour and in west direction is 42.42 miles/hour.
