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?

Yareli Bowman

Yareli Bowman

Open question

2022-08-21

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?

Answer & Explanation

uglasiteveh

uglasiteveh

Beginner2022-08-22Added 6 answers

1 m i l e = 1609.344 m
1 h o u r = 3600 s e c
Gravitational 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 N
Mass of the car = M
W = M g
8.91 x 10 4 = M ( 9.81 )
M = 9.083 × 10 3 k g
Initial speed of the car = V 1 = 73.1 m p h = 73.1 × ( 1609.344 3600 ) m / s = 32.678 m / s
Final speed of the car = V 2 = 28.5 m p h = 28.5 × ( 1609.344 3600 ) m / s = 12.74 m / s
Distance the car coasts along the ramp = L = 411 m
Height gained by the car = H = 14.3 m
Average 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 N
Magnitude of the average drag force exerted on the car = 6.906 kN

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