BITSAT 2011 Paper

The velocity of the car is given as, vc=30ms−1
And the velocity of ball with respect to the car is given as, vbc=20ms−1
Now we need to find the velocity of the ball with respect to the car with its components.
vbc=20‌cos‌60∘‌i+20‌sin‌60∘‌j
⇒vbc=20×‌

1

2

i+20×‌

√3

2

j
∴vbc=10i+10√3j
Now, we know that,
vbc=vb−vc
⇒vb=vbc+vc
⇒vb=10i+10√3j+30i
∴vb=40i+10√3j
Now we need to find the angle of projection. tan‌θ=‌

10√3

40

∴θ=tan−1(‌

√3

4

)
Therefore, the required value of the angle of projection is tan−1(‌

√3

4

).
Hence, option (B), i.e. tan−1(‌

√3

4

) is the correct choice of the given question.