Exam1-soln

Exam1-soln - Problem 1. Solution: In order to solve this...

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

View Full Document Right Arrow Icon
Problem 1. Solution: In order to solve this problem, it is simplest to determine the absolute velocity vector for each projectile when it begins its fight. Once we have established what the initial velocities are, we can compute the projectiles’ positions from d 2 r /dt 2 = g k . Let subscripts h and t denote the Humber and the tank, respectively. Also let subscripts b and a denote the shell buster and the artillery shell, respectively. We are given the velocities of each projectile relative to the vehicle from which it is launched, and the given velocities are v b/h = v cos φ i + v sin φ j and v a/t = 3 V cos φ i + 3 V sin φ j The vehicles’ velocity vectors are v h = V i and v t = 1 2 V i Therefore, the initial values of the projectiles’ velocity vectors are v b = v h + v b/h =( V + v cos φ ) i + v sin φ j v a = v t + v a/t = w 1 2 V + 3 V cos φ W i + 3 V sin φ j The equations governing the motion of the shell buster are d 2 x b dt 2 =0; x b (0) = 0 , ˙ x b (0) = V + v cos φ d 2 z b dt 2 = g ; z b (0) = 0 , ˙ z b (0) = v sin φ Solving, we find x b ( t )=( V + v cos φ ) t and z b ( t )= vt sin φ 1 2 gt 2 The equations governing the motion of the artillery shell are d 2 x a dt 2 x a (0) = L, ˙ x a (0) = w 1 2 V + 3 V cos φ W d 2 z a dt 2 = g ; z a (0) = 0 , ˙ z a (0) = 3 V sin φ Solving, we find x a ( t L w 1 2 V + 3 V cos φ W t and z a ( t 3 V sin φ 1 2 2 (a) The projectiles meet when x a = x b and z a = z b . Equating the vertical coordinates tells us that
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/11/2011 for the course AME 301 taught by Professor Shiflett during the Spring '06 term at USC.

Page1 / 5

Exam1-soln - Problem 1. Solution: In order to solve this...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online