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.

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 angl class=

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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

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