Please answer both and show work. Thanks Given the simultaneous launch condition

Question

Please answer both and show work. Thanks

Given the simultaneous launch conditions shown, determine the relative velocity of A with respect to B at one second after launch. Also determine the relative acceleration 1. 10 m/s B 10 m/s 60° 30° 2. At the instant shown, the bicyclist at A is traveling at 7 m/s around the curve on the race track while increasing his speed at 0.5 m/s2. The bicyclist at B is traveling at 8.5 m/s along the straight-a-way and increasing his speed at 0.7 m/s. Determine the relative velocity and relative acceleration of A with respect to B at this instant. Ug = 8.5 m/s = 7 m/s 50 m 50 m 40°

Explanation / Answer

1.

Vax = velocity of A along X-direction = 10 cos60 = 5 m/s

Vay = velocity of A along Y-direction = 10 Sin60 = 8.66 m/s

Vbx = velocity of B along X-direction = 10 cos30 = 8.66 m/s

Vby = velocity of B along Y-direction = 10 Sin30 = 5 m/s

relative velocity along X-direction

Vbax = Vbx - Vax = 8.66 - 5 = 3.66 m/s

relative velocity along Y-direction

Vbay = Vby - Vay = 5 - 8.66 = - 3.66 m/s

net relative velocity is given as

Vrel = sqrt(V2bax + V2bay) = sqrt((3.66)2 + (- 3.66)2) = 5.2 m/s

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