Answer
\[ \alpha = 15 \text{ or } 75 \]
Work Step by Step
Step 1 Given: \[ v_0 = 800, \quad s_0 = 0, \quad x_{\max} = 10000 \] Step 2 Since: \[ v = v_0 \cos(\alpha) t = 800\cos(\alpha)t \] and \[ y = s_0 + v_0\sin(\alpha)t - \frac{1}{2}gt^2 = (800\sin(\alpha)t - 16t^2) \] Step 3 To find the horizontal distance traveled, put \(y = 0\), then we get \(t = 0\) and \(t = 50\sin(\alpha)\), then: \[ x_{\max} = {800\cos(\alpha)(50\sin(\alpha))} = {20000\sin(2\alpha)} \] \[ 10000 = 20000\sin2\alpha \] Then: \[ 2\alpha = 30 \text{ or } 150 \Rightarrow \alpha = 15 \text{ or } 75 \] Result \[ \alpha = 15 \text{ or } 75 \]
