Question

A ball is thrown with an angle of 12 degrees to the horizon with a speed of 15m/s. What are it's vertical and horizontal components

Answer 1

A ball is thrown with an angle of 12 degrees to the horizon with a speed of $15\mathrm{m / s}$ . What are its vertical and horizontal components

Solution:

$V_{0} = 15\frac{m}{s} -$ initial velocity of the stone;

$\alpha = 12{}^{\circ} - \text{angle, above the horizontal, of the stone's initial velocity;}$

Horizontal and vertical components from the right triangle ABC:

$\Delta ABC: \cos \alpha = \frac{V_x}{V_0}$

$V_{x} = V_{0} \cdot \cos \alpha = 15\frac{m}{s} \cdot \cos 12{}^{\circ} = 14.7\frac{m}{s}$

$\Delta ABC: \sin \alpha = \frac{V_y}{V_0}$

$V_{y} = V_{0} \cdot \sin \alpha = 15\frac{m}{s} \cdot \sin 12{}^{\circ} = 3.1\frac{m}{s}$

Answer: Horizontal component: $V_{x} = 14.7 \frac{m}{s}$ , vertical component $V_{y} = 3.1 \frac{m}{s}$