This question has been asked a lot, but I still dont fully understand! Thank you

Question

This question has been asked a lot, but I still dont fully understand! Thank you!

A truck of mass mA moving at unknown velocity collides head-on a level road with a parked SUV of mass mB whose parking brakes are engaged. Upon collision, the bumpbers of the two vehicles stick together, and the mangled wreckage skids a distance d before comming to a full stop. The skid marks on the road are from that of the SUV only, indicating the truck never braked at all. If the coefficients of friction between the tires and ther oad are 0.7 and 0.9 for kinetic and static, respectivel, determine the initial speed of the truck just prior to the collision from the data:

mA (truck) = 3000 kg mB (SUV) = 2500 kg d= 42 m

a) Determine the initial speed of the truck just prior to the collision

b) Suppose the collision time interval at delta t was 0.090 seconds. Dtermine the average net-force during the 0.080 seconds on a 50 kg passenger in the SUV. Convert the net force to g-force

Explanation / Answer

here,

mA = 3000 kg

mB = 2500 kg

d = 42 m

let their combined speed be v

uk = 0.7

deaccelration due to friction , a = - uk*g = - 0.7 * 9.8

a = -6.86 m/s^2

v^2- u^2 = 2*d*a

v^2 = 2*42*6.86

v = 24 m/s

let the velocity of truck before be v'

using conservation of momentum

mA*v' = ( mA + mB) *v

v' = 44 m/s

the initial speed of the truck is 44 m/s

(b)

mass of passanger , m = 50 kg

time taken , t = 0.09 s

the average net force on the passanger , f = impulse /time

f = m*v/t = 50 * 24 /0.09

f = 13333.33 N

the average net force on the passanger is 13333.33 N

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