Having given up on the truck, Bob and Jane arrive at their lab in Cape Canaveral

Question

Having given up on the truck, Bob and Jane arrive at their lab in Cape Canaveral. "If Smeevenstein ransacked our lab at home, then whatever he took must be at his headquarters, " Jane figures as Bob primes the rocket, "Pack lightly. We're headed to Antigua." "Ooh, " says Bob. "I do love butter bread." Their rocket is a two-stage Pegasus-class booster and glider combination with a total mass of M = 6.70 Times 10^3kg without fuel. After launch, the rocket accelerates upward, burning all of its fuel to a velocity of 330 m/s. After the fuel burns out, the booster m_boost = 4.70 Times 10^3kg is ejected at an angle of 90 degree and a speed of 180 m/s. What is the magnitude and direction of the glider after the separation?

Explanation / Answer

let Vfx and vfy are the components of vf

Apply conservation of momentum in x-direction

6.7*10^3*330 = 2*10^3*vfx

==> vfx = 6.7*330/2

= 1105.5 m/s

Apply conservation of momentum in y-direction

4.7*10^3*180 = 2*10^3*vfy

==> vfx = 4.7*180/2

= 423 m/s

so, vf = sqrt(vfx^2 + vfy^2)

= sqrt(1105.5^2 + 423^2)

= 1184 m/s <<<<<<-----------Answer

direction : theta = tan^-1(vfy/vfx)

= tan^-1(423/1105.5)

= 20.94 degrees <<<<<<-----------Answer

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

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