{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

p0610

# p0610 - at the time of the explosion m d 2 z dt 2 = − mg...

This preview shows pages 1–2. Sign up to view the full content.

6.10. CHAPTER 6, PROBLEM 10 291 6.10 Chapter 6, Problem 10 Problem: Arocke to fmass m is launched vertically and reaches a height H with speed v o when it explodes. Part A has mass 2 5 m and, at time τ after the explosion, it strikes the ground a distance H west of the rocket’s launch point. Part B has mass 3 5 m . (a) If Part B’s height above the ground is 5 6 H when Part A strikes the ground, what is the velocity v o ? Letting g denote gravitational acceleration, express your answer as a function of τ , g and H . (b) Compute the velocity v o in km/hr for H =3 km and τ =90 sec. Solution: We appeal to Newton’s Second Law to solve for this two-particle system. (a) The only external force acting is gravity. So, the vertical position of the center of mass satisfies the following differential equation and initial conditions (with

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: at the time of the explosion). m d 2 z dt 2 = − mg, z (0) = H, ˙ z (0) = v o The solution is z ( t ) = H + v o t − 1 2 gt 2 The center of mass is defined by z ( t ) = 1 m } 2 5 mz A ( t ) + 3 5 mz B ( t ) ] Now, Part A strikes the ground when z A ( τ ) = 0 , and this equation simplifies to z B ( τ ) = 5 3 z ( τ ) = 5 3 H + 5 3 v o τ − 5 6 g τ 2 We are given z B ( τ ) = 5 6 H . Thus, 5 6 H = 5 3 H + 5 3 v o τ − 5 6 g τ 2 = ⇒ 5 3 v o τ − 5 6 g τ 2 − 5 6 H = 0 Solving for v o yields v o = g τ 2 − H 2 τ 292 CHAPTER 6. SYSTEMS OF PARTICLES (b) For the given values of H = 3 km = 3000 m and τ = 90 sec, we have v o = (9 . 807 m / sec 2 )(90 sec) 2 − 3000 m 2(90 sec) = 424 . 65 m / sec = 1529 km / hr...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

p0610 - at the time of the explosion m d 2 z dt 2 = − mg...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online