Rankers Physics
Topic: Kinematics
Subtopic: Ground to Ground Projectile

A particle is fired with velocity u making an angle θ with the horizontal. What is the change in velocity when it is at the highest point :
u cosθ
u
u sinθ
(u cosθ-u)

Solution:

At the highest point of its trajectory, the vertical component of the velocity becomes zero, while the horizontal component remains unchanged.

- Initial velocity: \( u \)
- Horizontal component: \( u_x = u \cos \theta \)
- Vertical component: \( u_y = u \sin \theta \)

At the highest point:
- Vertical velocity: \( u_y = 0 \)
- Horizontal velocity: \( u_x = u \cos \theta \)

The change in velocity is only in the vertical direction, from \( u \sin \theta \) to 0.

So, the change in velocity is:

\[
\Delta v = u \sin \theta
\]

Thus, the change in velocity is \( u \sin \theta \).

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