Express the vector described below. Give exact values for the components. Show all work. A ball is thrown with an initial velocity of 70 feet per second at an angle of 60° with the horizontal.

Solution
A ball thrown with initial velocity of 70ft/s
[tex]\begin{gathered} \text{ initial velocity=70}\frac{ft}{s} \\ u=\frac{70ft}{s} \end{gathered}[/tex]Horizontal component = Ucosθ, Vertical component = Usinθ
[tex]\begin{gathered} \text{Horizontal component = Ucos}\theta \\ =70\cos 60 \\ =70(\frac{1}{2}) \\ =\frac{35ft}{\sec} \end{gathered}[/tex]Therefore the value of the horizontal component = 35ft/sec
[tex]\begin{gathered} \text{Vertical component = U}\sin \theta \\ =70\sin 60 \\ =70(\frac{\sqrt[]{3}}{2}) \\ =\frac{60.62ft}{\sec} \\ \approx\frac{61ft}{\sec } \end{gathered}[/tex]Therefore the value of the vertical component = 61ft/sec