A ball is moving with velocity 5 m/s in a direction which makes an angle of 30° with horizontal (i. e. with positive x-direction). This ball hits a vertical wall and gets reflected in a direction which makes an angle of 60° with the vertical (i. e. with positive y-direction) and moves with the same magnitude i. e. 5 m/s: a. Find components of the initial and reflected velocities.
b. Show the vector representing the change in velocity of the ball.
c. Find the magnitude of the change in velocity.

Explanation:

(a)

From the given information:

The initial velocity = 5 m/s

The direction of the angle θ = 30°

Therefore, the component along the x-axis =

The component along the y-axis =

To find the final velocity( reflected velocity)

using the same magnitude

The angle from the x-axis can be

= 150°

Thus, the component along the x-axis =

The component along the y-axis =

(b)

The velocity can be written as in vector form.

 ----  (1)

The reflected velocity in vector form can be computed as:

 --- (2)

The change in velocity =

(c)

The magnitude of change in velocity =

= 8.66 m/s

e) none of the above answers are correct

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