Question

Two trains of pass through the same intersection at different times. Knowing that Train B accelerates from rest at 100 m/min2 and reaches the crossing 10 min after Train A passed through. Determine the relative velocity of Train B with respect to Train A and the distance between the fronts of each train 2 min after Train B passes through the intersection. Express your answer in vector notation. 72 km/h A O B 30°

Please show all work and steps. Any help will be appreciated and thank you for your time!

Train A's distance is not given.

Answer 1

Calculate the velocity of train B after 10+2=12 min. Vg = 1g + at = 0+(100) (10 + 2) = 1200 m/min = 20 m/s 73 = (v, cos 30°) + (ve sin 30%) =((20) cos 30)î +(20) sin 309) = (17.32)î +(10) + Calculate the relative velocity of train B with respect to train A. VB4 = vg - ={(173218 +(10);}-{-(12-1)}} ={(17.32) +(10)}}-{-(20)f} = (37.32)î +(10) Calculate the velocity of train B after 10 min. Vg = lg + at = 0+(100) (10) = 1000 m/min Calculate the distance travelled by train B after passing through intersection. OB = výr+şar? =(1000)(2)+2(100)(2) 2= 22 Consider the figure.

B 72 km/h 150° 30 Calculate the distance covered by train A after 10+2=12 min. 5 04=v, xt = 72 = x(10+2) = 240m 18 Calculate the distance between fronts of each train. (04) +(OB)? -(AB? cos 150º = 2(04)(OB) (AB)? =(OA)? +(OB)? -2(04)(OB)cos150° AB = (04)* +(OB) – 2(04)(OB) cos150° = (240)* +(2200)* – 2 (240)(2200) cos 150° = 2410.83 m