Answer to Question #183655 in Classical Mechanics for joseph

Question

1.Car A rounds a curve of 129-m radius at a constant speed of 42 km/h. At the instant represented, car B is moving at 83 km/h but is slowing down at the rate of 4.9 m/s². Determine the velocity and acceleration of car A as observed from car B.

v_A/B =( _ i + _j) m/s

a_A/B =( _i + _j) m/s²

2.The jet transport B is flying north with a velocity v_B = 505 km/h when a smaller aircraft A passes underneath the transport headed in the 68^° direction shown. To passengers in B, however, A appears to be flying sideways and moving east. Determine the magnitudes of the actual velocity of A and the velocity which A appears to have relative to B.

Aircraft A is going in northeast direction

v_A = _ km/h

v_A/B =  _ km/h

Answer 1

1)

$v_{A/B}=\frac{83}{3.6}\vec i+\frac{4.9\cdot 129\cdot 3.6}{42}\vec j=23.056\vec i+54.180\vec j,$

$a_{A/B}=\frac{83\cdot 42}{3.6\cdot 3.6\cdot 129}\vec i+4.9\vec j=2.085\vec i+4.900\vec j.$

2)

$v_A=\frac{v_B}{\cos 68°}=1348.081~\frac{km}{h},$

$v_{A/B}=v_B\tan 68°=1249.919~\frac{km}{h}.$