Answer to Question #183660 in Classical Mechanics for joseph

Question

Answers should be in three decimal numbers

1.The car A has a forward speed of 23 km/h and is accelerating at 2.7 m/s². Determine the velocity and acceleration of the car relative to observer B, who rides in a nonrotating chair on the Ferris wheel. The angular rate Ω = 3.8 rev/min of the Ferris wheel is constant.

v_A/B = (  _i +  _j) m/s

a_A/B = (  _i + _j) m/s²

2. Starting from the relative position shown, aircraft B is to rendezvous with the refueling tanker A. If B is to arrive in close proximity to A in a 3.0-minute time interval, what absolute velocity vector should B acquire and maintain? The velocity of tanker A is 257 mi/hr along the constant-altitude path shown.

y = 9350'

x = 2360'

v_B = (  _i +  _j) mi/hr

Answer 1

1)

$v_{A/B}=\frac{23}{3.6}\vec i+\frac{2.7\cdot 60}{2\cdot 3.14\cdot 3.8}\vec j=(6.389\vec i+6.788\vec j)\frac ms,$

$a_{A/B}=\frac{23\cdot 2\cdot 3.14\cdot 3.8}{3.6\cdot 60}\vec i+2.7\vec j=2.541\vec i+2.700\vec j.$

2)

$v_B=\frac{\sqrt{9350^2+2360^2}\cdot 60}{3600\cdot 3}\vec i+257\vec j=(53.574\vec i+257.000\vec j)~\frac{mi}{hr}.$