Question

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

Answer 1

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:

`r=(1)/(32)v^2_o\sin (2\theta)`

Replacing the variables with the given values, we obtain:

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

One possible value for theta is 22.98°.