Far out in space, a bored astronaut fires an antique gun at a sack of rocks (mas

Question

Far out in space, a bored astronaut fires an antique gun at a sack of rocks (mass M). The bullet (mass m) bounces around inside the sack a few times, eventually emerging with a reduced, but still high, speed. As the bullet flies off into space, the astronaut remembers with dismay that it was a priceless historical artifact. Fortunately, the astronaut knows the initial speed vo of the bullet, and that the sack was initially at rest but after being hit was found to be moving with speed Vs at angle , as shown in the diagram. In what direction should the astronaut pursue the bullet, assuming that he starts from the initial location of the sack, and what minimum speed vb must he go faster than in order to catch up with it? Use the numerical values given below, and enter the direction as an angle b measured clockwise from the x-axis m= 0.0250 kg =45.0 kg vo = 1550 m/s Vs = 0.655 m / s = 24.8 before after Number Number m/s

Explanation / Answer

Applying momentum conservation for bullet-sack system during collision,

Pi = Pf

along x axis.

(0.0250) (1550) + 0 = (45)(0.655)cos24.8 + (0.0250)(vB) cos(theta)

vB cos(theta) = 12 ....... (i)

along y - axis,

0 = (45)(0.655) (sin24.8) - (0.0250)(vB)sin(theta)

vB sin(theta) = 12.36 .... (ii)

(ii) /(i) => tan(theta) = 12.36 / 12

theta = 46 deg ........Ans

vB = 17.2 m/s .......Ans

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

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