At the intersection of Texas Av and conversely believe a yellow, compact car wit

Question

At the intersection of Texas Av and conversely believe a yellow, compact car with mass 50 kg traveling cost and university collides with a pickup truck with most 1900 kg what traveling month an and a red light the two stick together as a result of the collision and, after the collision, the is shading at 16.0 m/s in the direction 29.0 Degree east of north. The collision accrue during a heavy rainstorm you come ignore fraction forces between the vehicles and the wet road. Calculate the speeds of the car and the truck before collision.

Explanation / Answer

Given

mc = 250 kg, mt = 1700 kg

car moving towards east and the truck moving towards north

so the momentum vectors of car and truck are

   mc*u1c i+mc*u1c j = 250*u1ci + 0 j

for truck

   mt*u1t i + mt*u1t j = 0 i +1700*u1t j

after the collision they stick together and moving with velocity 16 m/s in a direction of 34 degrees east of north so the angle with the horizontal is 56 degrees

now the final momentum vector is

   (mc+mt)v cos theta i +(mc+mt) v sin theta j

  
   (250+1700)16 cos56 i + (250+1700)16 sin56 j

  
   17446.81859 i + 25865.97226 j

equating these with initial momentum

   17446.81859 i + 25865.97226 j = 250*u1c i +1700*u1t j

   u1c = 17446.81859/250 m/s = 69.78727436 m/s

   u1t = 25865.97226 / 1700m/s = 15.2152778 m/s

the initial velocities of car and pick up trucks are

   69.78727436 m/s,15.2152778 m/s.

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