Question

One of the rectangular component of the velocity is 10m/s in a direction inclined at an angle of 60 with the direction of velocity. The other component is

Answer 1

Explanation:

given velocity v = 20 m/s

let the given rectangular component is

cos somponent, so 10 = v cos x

so, other component will be sin component

i.e., v sin x

or, 10 = 20 cos x

or, cos x = 1/2

and as sin^2 x + cos^2 x = 1

or, 1 - cos^2 x = sin^2 x

or, 1 - (1/2)^2 = sin^2 x

so, sin x = sqrt( 1 - 1/4)

or, sin x = sqrt(3/4)

so, rectangular component is

20 sin x = 20 sqrt(3/4)

= 10 sqrt3

= 17.32 m/s

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Answer 2

The other rectangular component of the velocity is 10√3 m/s.

One of the rectangular component of the velocity is 10m/s in a direction inclined at an angle of 60° with the direction of velocity.

We have to find the other component of the velocity.

It can be understood easily if we draw a rough diagram of it.

See attached figure, Here we see that a velocity , v is projected at an angle 60° with the horizontal. Here ABCD is a rectangle and velocity v is diagonal of it.

From ΔADC,

⇒ cos60° = CD/AC

⇒ cos60° = CD/v

⇒ CD = v cos60°

Here BC is the rectangular component of the velocity in a direction.

i.e., BC = v cos60° = 10 m/s [ given ]

⇒   v = 10/cos60° = 10/(1/2) = 20 m/s ...(1)

From ΔABC,

⇒ sin60° = BC/AC

⇒ sin60° = BC/v

⇒ √3/2 = BC/20   [ from equation (1) ]

⇒ BC = 10√3 m/s

Here BC is the other rectangular component of the velocity.

Therefore the other rectangular component of the velocity is 10√3 m/s.

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