Question

= *Chapter 2, Practice Problem 2/088 Two ships A and B are moving with constant speeds VA 24 m/s and ve = 26 m/s, respectively, along straight intersecting courses. The navigator of ship B notes the time rates of change of the separation distance r between the ships and the bearing angle 8. If r = 84 m and 2 = 113º, what does the navigator measure for , , and Ö? Check that * -ró= 0 and rö + 210 = 0. VA COS UB 005 B 65 Answers: i= 1 m/s j*?m/s2 0 1-3 rad/s = = ë - 4 rad/s2

Answer 1

Sot Giren, VA = 24 see VB = 36 msee %= 84m (NA) = VACOS 48 VA S748" O = 113 VAV (VA)v = Va co$671 (VA) A 48 (ve. Dit (VB) = VB sinet A We v 84mar 113° 48 VB 67 67 65 B s(NO) and VB Resolving the VA horizontally of vertically with reapest to the line AB. Rate of change of seperation (i): (VA) H+ (Ve)h Calong the AB) [ The components (horizontal) of VA and ro to each other are opposite = 24 cos 48 + 26 cos 67 = 26.018 m/sec

The angular velocity (6): find the relati In order to angular velocity, take the vertical components VA and VB As we know that V8)v-(VBY જ ઉં (VA)v [: rez velocity Ó VB) o =-24 sin 48+26 Sin67 84 -0.07259 rad/see -0.0726 6 relations, from given 8-88=0 jo v 88² = 84 (0.07262 % = 0.44 27 m/s² -zió -0.0453 Ô = röter Q = 0.04531 Bigud leny 26.218*15 % = 0.4427 m/s 820.0726 rad) see