Question

questions 17 - 19:
a football is kicked with a speed of 18 m/s at an angle of 65° to the horizontal.

1. what are the respective horizontal and vertical components of the initial velocity of the football?

(a) 7.6 m/s, 16 m/s b) 16 m/s, 7.6 m/s c) 8.4 m/s, 13 m/s
d) 13 m/s, 8.4 m/s e) 9 m/s, 9 m/s

Explanation:

Step1: Calculate horizontal component

The formula for horizontal component \(v_x = v\cos\theta\). Given \(v = 18\ m/s\) and \(\theta=65^{\circ}\), then \(v_x=18\cos65^{\circ}\approx18\times0.423 = 7.6\ m/s\).

Step2: Calculate vertical component

The formula for vertical component \(v_y = v\sin\theta\). Given \(v = 18\ m/s\) and \(\theta = 65^{\circ}\), then \(v_y=18\sin65^{\circ}\approx18\times0.906=16.3\approx16\ m/s\).

Answer:

A. \(7.6\ m/s\), \(16\ m/s\)