A missile silo is used to launch military rockets vertically upward out of the s

Question

A missile silo is used to launch military rockets vertically upward out of the silo, giving the rocket an initial speed of 79.4 m/s at ground level. As the rocket clears the silo, the engines fire, and the rocket accelerates upward at 3.90 m/s2 until it reaches an altitude of 1,080 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of 9.80 m/s2. (You will need to consider the motion while the engine is operating and the free-fall motion separately. Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.) (a) Determine the velocity of the rocket (in m/s) at the end of the engine burn time and also the burn time (in s). (For the velocity, indicate the direction with the sign of your answer.) velocity at end of engine burn time v = m/s engine burn time t = s (b) Determine the maximum altitude of the rocket (in m) and the total time (in s) for the rocket to reach this altitude from ground level. maximum altitude y = m time to reach maximum altitude t = s (c) Determine the rocket's velocity (in m/s) just before ground impact and its total time of flight (in s). (For the velocity, indicate the direction with the sign of your answer.) velocity just before ground impact v = m/s total time of flight t = s

Explanation / Answer

Case A: when the engine burns:

initial velocity = 79.4 m/s , acc = 3.9 m/s2 , tot. height= 1080 m

so velocity attained at the time when engine fails -> v2=u2+2aS -> v = 121.36 m/s

Also time during which engine burns (during which it reaches height of 1080m) => S=ut+1/2gt2 =>

t= 131 s

Case B: when engine fails:

the missile continues to go further because of inertia until its velocity becomes zero, so to get the distance travelled we use v2 = u2 -2gS -> 0=121.362 -2*9.8*S -> S = 751.4m

also to find the time, we use the formula v=u-gt ->t= 12.4 s

So total distance(max height') = 1080+751.4= 1831.4m and total time taken = 131+12.4 = 143.4 s

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