Test Your Skill

1. A small sports car, weighing 2345 pounds (#) including occupants, is driving eastbound on a mountain roda. A full-size sedan is driving westbound on the same road. The sedan weighs 3695 pounds (#) including load and ocupants. Teh sedan drifts over the centerline after rounding a curve and teh two vehicles collide in a head-on collision. The impact is such that the vehicles come to rest in their impact positions. Given that the speed of the sedan was 45 miles per hour (mph), determine an estimate for the sports car's speed.

Answer

1. We will let the sports car be denoted by m₁ and the sedan by m₂
   
   m₁ = 2345# / 32.2f/s² = 72.82 #s²/ft
   
   m₂ = 3695# / 32.2f/s² = 114.75 #s²/ft

   Now:
   
   m₁v₁ + m₂v₂ = m₁u₁ + m₂u₂
   
   m₁v₁ + m₂v₂ = 0 (post collision velocities are 0 f/s)
   
   v₁ = -m₂v₂ / m₁
   
   v₁ = -(114.75 #s²/ft)(-66f/s) / 2.82 #s²/ft
   
   v₁ = 104 f/s or approximately 70 mph

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