You have designed a rocket to be used to sample the localatmosphere for pollutio

Question

You have designed a rocket to be used to sample the localatmosphere for pollution. It is fired vertically with aconstant upward acceleration of 20 m/s2. After 27seconds, the engine shuts off and the rocket continues rising (infreefall) for a while. (Neglect any effects due to air resistance.)The rockets eventually stops rising and then falls back to theground. You want to get a sample of air that is 25 km above theground. 1. What is the highest point (in km) your rocketreaches? Did you reach your height goal? 2. Determine the total time the rocket is in theair. 3. Find the speed of the rocket just before it hits theground. You have designed a rocket to be used to sample the localatmosphere for pollution. It is fired vertically with aconstant upward acceleration of 20 m/s2. After 27seconds, the engine shuts off and the rocket continues rising (infreefall) for a while. (Neglect any effects due to air resistance.)The rockets eventually stops rising and then falls back to theground. You want to get a sample of air that is 25 km above theground. 1. What is the highest point (in km) your rocketreaches? Did you reach your height goal? 2. Determine the total time the rocket is in theair. 3. Find the speed of the rocket just before it hits theground.

Explanation / Answer

1. the speed before the engine shuts off is: v = at =20m/s2*27s = 540m/s the height before engine shuts off is: h = (1/2)at2= 0.5*20m/s2*(27s)2 = 7290 m after the enegin off, it will continue go up h highand h = v2 /2g = (540m/s)2/(2*9.8m/s2) ˜ 14878 m total high is: H=h+h=7290m+14878m = 22168 m=22.168km the highest point is 22.168km it is not reach the 25km goal. 2. the time after engine shuts off to the highest point is: t2 =v/g = 540m/s / 9.8m/s2 = 55.1 s the time from highest point fall to ground is t3 and H = (1/2)g(t3)2 => t3 = (2*H/g) =(2*22168m/9.8m/s2) = 67.3 s total in air time is: T = 27s + 55.1 s + 67.3 s = 149.4s 3. at highest point, speed is 0, and time to fall ist3=67.3s the speed before hit the ground is: vf = g*(t3) = 9.8m/s2*67.3s = 659.54m/s .

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