A 89.1-kN car is travelling at 73.1 mph when the driver decides to exit the freeway by going up a ramp. After coasting 411 m along the exit ramp the car's speed is 28.5 mph, and it is h = 14.3 m above the freeway. What is the magnitude of the average drag force exerted on the car?

Question

A 89.1-kN car is travelling at 73.1 mph when the driver decides to exit the freeway by going up a ramp. After coasting 411 m along the exit ramp the car&#039;s speed is 28.5 mph, and it is h = 14.3 m above the freeway. What is the magnitude of the average drag force exerted on the car?

uglasiteveh · Accepted Answer

1  m  i  l  e  =  1609.344  m  1  h  o  u  r  =  3600  s  e  cGravitational acceleration   =  g  =  9.81  m      /        s    2  Weight of the car   =  W  =  89.1  k  N  =  89.1  ×      10    3    N  =  8.91  ×      10    4    NMass of the car = M  W  =  M  g  8.91  x      10    4    =  M  (  9.81  )  M  =  9.083  ×      10    3    k  gInitial speed of the car   =      V    1    =  73.1  m  p  h  =  73.1  ×  (      1609.344    3600    )  m      /    s  =  32.678  m      /    sFinal speed of the car   =      V    2    =  28.5  m  p  h  =  28.5  ×  (      1609.344    3600    )  m      /    s  =  12.74  m      /    sDistance the car coasts along the ramp   =  L  =  411  mHeight gained by the car   =  H  =  14.3  mAverage drag force on the car   =      F    D  By conservation of energy the initial kinetic energy of the car is equal to the final potential energy plus kinetic energy of the car plus the energy lost to work done against the drag force,            M              V        1        2              2    =  M  g  H  +            M              V        2        2              2    +      F    D    L  (  9.083  ×      10    3    )  (  32.678      )    2        /    2  =  (  9.083  x      10    3    )  (  9.81  )  (  14.3  )  +  (  9.083  ×      10    3    )  (  12.74      )    2        /    2  +      F    D    (  411  )      F    D    =  6.906  ×      10    3    N      F    D    =  6.906  k  NMagnitude of the average drag force exerted on the car = 6.906 kN

A 89.1-kN car is travelling at 73.1 mph when the driver decides to exit the freeway by going up a ramp. After coasting 411 m along the exit ramp the car\'s speed is 28.5 mph, and it is h = 14.3 m above the freeway. What is the magnitude of the average drag force exerted on the car?

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