A 1600 kg sedan goes through a wide intersection traveling from north to south w

Question

A 1600 kg sedan goes through a wide intersection traveling from north to south when it is hit by a 2200 kg SUV traveling from east to west. The two cars become enmeshed due to the impact and slide as one thereafter. On-the-scene measurements show that the coefficient of kinetic friction between the tires of these cars and the pavement is 0.750, and the cars slide to a halt at a point 5.48 m west and 6.55 m south of the impact point.

Part A

How fast was sedan traveling just before the collision?

Part B

How fast was SUV traveling just before the collision?

Explanation / Answer

let y and x be speeds of sedan and SUV respectively before collision

momentum in north to south = 1600y

momentum in east to west = 2200x

distance travelled after collision = sqrt(5.48^2 + 6.55^2) =8.54007611207 m

8.54007611207 = 0.5 * 0.750*9.81*t^2

t=1.52363427253 s

0 = u - 0.750*9.81 * 1.52363427253

u= 0.750*9.81 * 1.52363427253 =11.2101391601m/s

in north south

(1600y/(2200+1600)) *1.52363427253 -0.5*0.75*9.81*1.52363427253 ^2 = 6.55

y=23.5220035493 m/s

in east west

(2200x/(2200+1600)) *1.52363427253 -0.5*0.75*9.81*1.52363427253 ^2 = 5.48

x=15.9007047662 m/s

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