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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