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A baseball leaves a bat at an angle of O in reference to the horizontal. The initial velocity is vo = 91 feet per second. The baseball is caught 186 feet away. Find one1value of Oif the range of the baseball is given by the equation r = vo sin(20). Express your answer in degrees or radians rounded to the nearest hundredth.32

A baseball leaves a bat at an angle of O in reference to the horizontal The initial velocity is vo 91 feet per second The

Answer :

For this problem, we are given an equation that describes the range of a baseball, and we need to solve it for the angle theta. The equation is shown below:

[tex]r=\frac{1}{32}v^2_o\sin (2\theta)[/tex]

Replacing the variables with the given values, we obtain:

[tex]\begin{gathered} 186=\frac{1}{32}\cdot91^2\cdot\sin (2\theta) \\ 186=\frac{8281}{32}\cdot\sin (2\theta) \\ 5952=8281\cdot\sin (2\theta) \\ \sin (2\theta)=\frac{5952}{8281} \\ \sin (2\theta)=0.7188 \\ \arcsin (\sin (2\theta))=\arcsin (0.7188) \\ 2\theta=45.96º \\ \theta=\frac{45.96º}{2} \\ \theta=22.98º \end{gathered}[/tex]

One possible value for theta is 22.98°.

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