Question

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

3) A Greyhound bus is travelling at 60,
from Boston to New York city)
a. what is its velocity component
bat is its velocity component along the south direction?(5 pts)
h what is its component of speed along the west directionale
of speed along the west direction? (5 pts)
Bus travelling south west​

Answer 1

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

Step-by-step 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*\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*\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.