Question

a cannonball is fired with an initial velocity of 100. meters per second at an angle of 15.0° above the horizontal. what are the horizontal (v_x) and vertical (v_y) components of this velocity? (1) v_x = 96.6 m/s, v_y = 25.9 m/s (2) v_x = 25.9 m/s, v_y = 96.6 m/s (3) v_x = 76.0 m/s, v_y = 65.0 m/s (4) v_x = 65.0 m/s, v_y = 76.0 m/s

Explanation:

Step1: Calculate the horizontal component

The formula for the horizontal component of velocity is \(v_x = v\cos\theta\), where \(v = 100\space m/s\) and \(\theta=15^{\circ}\).

$$v_x = 100\times\cos(15^{\circ})$$

Using the value \(\cos(15^{\circ})\approx0.966\), we get \(v_x = 100\times0.966 = 96.6\space m/s\)

Step2: Calculate the vertical component

The formula for the vertical component of velocity is \(v_y = v\sin\theta\), where \(v = 100\space m/s\) and \(\theta = 15^{\circ}\).

$$v_y=100\times\sin(15^{\circ})$$

Using the value \(\sin(15^{\circ})\approx0.259\), we get \(v_y = 100\times0.259=25.9\space m/s\)

Answer:

1. \(v_x = 96.6\space m/s\), \(v_y = 25.9\space m/s\)