Question

Whound bus is travelling at 60 miles per hour on rte 95 going south west (for example travelling

Answer 1

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 $V_{x}$ of x axis and  $V_{y}$ of y axis.

$\vect{V}=\vec{V_{x}i}+\vec{V_{y}j}$

Where,

$V_{x}=|\vec{V}|\cos\theta$...(I)

$V_{y}=|\vec{V}|\sin\theta$....(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)

$V_{x}=|\vec{V}|\cos\theta$

Put the value into the formula

$V_{x}=60\times\cos45$

$V_{x}=42.42\ miles/hour$

(b). We need to calculate the velocity component in west direction

Using equation (II)

$V_{x}=|\vec{V}|\sin\theta$

Put the value into the formula

$V_{x}=60\times\sin45$

$V_{x}=42.42\ miles/hour$

Hence, The velocity component in south direction is 42.42 miles/hour and in west direction is 42.42 miles/hour.