(Solved): A military drone carries out the following mission: 1. Take off from sea level and ascend to a crui ...

A military drone carries out the following mission: 1. Take off from sea level and ascend to a cruising altitude of 9 miles. 2. Accelerate to a top speed of Mach 3 . 3. Fire a precision-strike missile at a designated ground target. Your task is to analyze the parameters of the mission as follows: (a) During stage 1, the vertical position of the drone is given by the equation, $y(t)=4.5\left(1-\cos \left(\frac{\pi }{210}t\right)\right)$ with $y$ in miles and $t$ in seconds. Determine the following: - How long does it takes the drone to reach its cruising altitude? - What is the max vertical speed the drone reaches? - What is the max vertical acceleration the drone experiences? (b) During stage 2, the horizontal velocity of the drone is given by the equation, $v_x(t)=\left(-0.25\ast 10^{-6}\right)x^4+\left(0.025\ast 10^{-3}\right)x^3+0.0425x^2+73.5$ with $v_x$ in $\mathrm{mph}$ and $t$ in seconds. Determine the following: - How long does it take the drone to reach top speed? - What is the max acceleration the drone experiences? - How much horizontal distance does the drone cover during stage 2?