Question

Colby participates in a rocket-launch competition in her high school. The goal is to launch a rocket with mass m = 2.3 kg [5 lbs] to a height no less than 50-m (164 ft) above ground.

a) What is the minimum momentum of the rocket as it leaves the launch pad?

b) Colby figured out three possible propulsion mechanisms that differ by the generated force F (“thrust”) and the time interval ∆t during which the force acts on the rocket [“burn time”]: Force F [N] Time interval ∆t [s] Propulsion #1 161 0.41 Propulsion #2 233 0.37 Propulsion #3 532 0.12 What is Colby’s best choice for the propulsion mechanism? Explain your reasoning!

c) Colby is excited about the successful launch of her rocket but is disappointed because the rocket is in air for only t1 = 3.1 s after the launch until it reaches the highest point. Explain Colby’s disappointment and calculate the air resistance acting on the rocket! Assume that the air resistance is constant.

d) Does Colby’s rocket meet the requirement of the contest?

e) The rocket returns to the ground at the time t2 = 6.5 s measured from the time of the launch. Calculate the impulse imparted on the rocket during the flight form the highest back to the ground. Find the velocity vector!] of the rocket just before it lands on the ground!

Answer 1

Ans: a) Consider the above given that Maximum height h = 50 m M = 2.3kg 2 42 - then 니 =) v²=42.2gh find speed at velocity V-O 29 h 29 h u = √2gh 12 (9.81)(50) 31.3 mis required momentum I u mu = 2-3 X 31.3 = 72kg mis the minimum momentum = 72kg mis b) impulse force x time F at mis Propulsion #1 =161 X 0.41 = 66.01 kg poopulsion #2 = 233 70.37 = 233 x 0.37 86.21 kg mis propulsion # 3 a 532 X0-12 63.84 kg mis of provide maximum Propulsion #2 is best case impulse best case { 233,0.37} -86 21 Chat momentum Mass Ĉ 2 3 3.1s time initial speed 86.21 37.5 mis U momentum 4 - 2. 3 Maximum height mass u 37.5 9 9.8 = 3.8s

petardation 2 = 4 37.5 = 12.1 m/s2 t 31 2 12.1 Retardation due to only air resistance g. 8 - 2.3 m/s Air Resistance = M (Retarda tion due to only air resistance) = 2.3 (2.3) = 5.29 N Air Resistance acting on 2 42 37.5 Jln the rocket is 5. 29 N d) h = 58. 11 m 2(12.1) .:. maximum height = 50 m. = 58. Ilm then colby's rocket height the colby's needs the requirement of context rocket es tz 6.5 s ah 2 h at? =) 2h sat t² 2 2 a = = 10.05 m/s2 2 (5811) (3.4 4) ² implese - M at = 2:3 (10.05) 3.4 = 78.6 kg mis velocity Vs at = 10.05 X 3.4 - 34.17 mis the velocity v=34.17 mis