The horizontal component of the initial speed of a particle projected at 30° to the horizontal is 50 m\(^{-1}\). If the acceleration of free fall due to gra...
Question 1 Report
The horizontal component of the initial speed of a particle projected at 30° to the horizontal is 50 m\(^{-1}\). If the acceleration of free fall due to gravity is 10 ms\(^{-2}\), determine its;
(a) initial speed;
(b) speed at the maximum height reached.
Answer Details
Projectile launched at 30 degrees with horizontal component 50 ms\(^{-1}\)
(a) Initial speed
The horizontal component is \(v_x = v\cos\theta\), so:
\[ v = \frac{v_x}{\cos\theta} = \frac{50}{\cos 30^\circ} = \frac{50}{0.8660} = 57.7\,\text{ms}^{-1} \](b) Speed at maximum height
At the highest point of the flight the vertical component of velocity is zero; only the horizontal component remains (it is unchanged throughout the motion). Therefore:
\[ v_{\text{top}} = v_x = 50\,\text{ms}^{-1} \]The speed at maximum height is \(50\,\text{ms}^{-1}\).
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