Solution:
To find the angle with the horizontal after 1.5 seconds, we calculate the horizontal and vertical components of velocity at that moment.
- Initial speed: \( u = 30 \, \text{m/s} \)
- Angle of projection: \( \theta = 30^\circ \)
- Horizontal component of velocity (remains constant):
\[
u_x = u \cos \theta = 30 \times \frac{\sqrt{3}}{2} = 15\sqrt{3} \, \text{m/s}
\]
- Vertical component of velocity after 1.5 seconds:
\[
u_y = u \sin \theta - g t = 30 \times \frac{1}{2} - 10 \times 1.5 = 15 - 15 = 0 \, \text{m/s}
\]
Since the vertical component is 0, the angle with the horizontal is:
\[
\text{Angle} = 0^\circ
\]
Thus, the angle with the horizontal after 1.5 seconds is \( 0^\circ \).
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