Question

A car is moving towards east with a speed of 25km/h. To the driver of the car, a bus

appears to move towards north with a speed of 25 3 / km h . What is the actual velocity

of the bus?

1) 0

50 / ,30 km h east of north 2) 0

50 / ,30 km h north of east

3) 0

25 / ,30 km h east of north 4) 0

25 / ,30 km h north of east
​

Answer 1

the car is moving towards east with a speed of 25 km/h. To the driver of the car, a bus appears to move towards north with a speed of  

25

√

3

k

m

/

h

. What is the actual velocity of the bus?

A

50

k

m

/

h

,

30

o

east of north

B

50

k

m

/

h

,

30

o

north of east

C

25

k

m

/

h

,

30

o

east of north

D

25

k

m

/

h

,

30

o

north of east

Solution

V

b

= velocity of bus

V

c

= velocity of car

V

b

c

=

25

√

3

k

m

/

h

r

now from relative velocity

|

→

V

b

|

=  

√

(

25

)

2

+

(

25

√

3

)

2

= 50km/hr

for direction  

t

a

n

θ

=

25

√

3

25

=

√

3

so  

′

θ

′

is from east direction  

Therefore it will be at 30' east of north

Hence (A) is correct