Question

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.

Answer 1

A ball thrown with initial velocity of 70ft/s

`\begin{gathered} \text{ initial velocity=70}(ft)/(s) \\ u=(70ft)/(s) \end{gathered}`

Horizontal component = Ucosθ, Vertical component = Usinθ

`\begin{gathered} \text{Horizontal component = Ucos}\theta \\ =70\cos 60 \\ =70((1)/(2)) \\ =(35ft)/(\sec) \end{gathered}`

Therefore the value of the horizontal component = 35ft/sec

`\begin{gathered} \text{Vertical component = U}\sin \theta \\ =70\sin 60 \\ =70(\frac{\sqrt[]{3}}{2}) \\ =(60.62ft)/(\sec) \\ \approx(61ft)/(\sec ) \end{gathered}`

Therefore the value of the vertical component = 61ft/sec