You have designed a rocket to be used to sample the local atmosphere for polluti

Question

You have designed a rocket to be used to sample the local atmosphere for pollution. It is fired vertically with a constant upward acceleration of 16 m/s^2. After 26 s, the engine shuts off and the rocket continues rising (in freefall) for a while. (Neglect any effects due to air resistance.) The rocket eventually stops rising and then falls back to the ground. You want to get a sample of air that is 17 km above the ground.

a)What is the highest point your rocket reaches?
b)Determine the total time the rocket is in the air.
c)Find the speed of the rocket just before it hits the ground.

Explanation / Answer

Acceleration upward: (16-9.8)m/s Distance upward before engine stops: y=1/2a(t^2) = 3.1*(26^2) = 2095.6m Velocity at that height: v = at = 6.2*26 = 161.2m/s Once it reaches this velocity, it will accelerate back toward the ground. Max height: v^2 = V0^2 + 2ay --> y = (v^2 - V0^2) / (2a) = /18.6 = 1397.1m y0 +y = max H = 1397.1+2095.6 = 3492.7m Time to max height = 2d/ (v-v0) +26s = 17.3+26 = 43.3s The other part of the time is the free fall from the max height to the ground: You need the end velocity first (unless you want to solve a quadratic, which I don't) v^2 = v0^2 + 2a y = 0 - 18.6(3492.7m) = 64964.2 v= -254.9m/s Now, the second part of the time = 2d / (v-v0) = 2(3492.7) / (254.9) = 27.4s total time = t1+t2 = 43.3s + 27.4s = 70.7s

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.