Hi

I got a question
Firstly Road conditions are good.
OK,

Bike Mass = 230 kg
Car mass = 1600 Kg
Initial Velocity Car = 0 km/h
Initial Velocity Bike = REQUIRED
After Accident Velocity CAR & BIKE = 0 km/h
Distance of CAR travell = 35 m north
Distance of Bike Travell = 35m north

Lets assume Momentum is conserved except for friction

Ok , now my question is what was the initial speed of the bike just before impact, assuming there was no braking etc .





_________|BIKE|-->|CAR| -------------35M--------------> |CAR&BIKE|

Thank you , if you could also share the formula you used

You need to provide more information - we need to know the coefficient of friction between the car/bike and the road. Obviously this depends on whether the car had its brakes applied, the condition of the road, was it on a hill, etc. So it's impossible to give you a definitive answer. However, under normal driving conditions a car traveling at 40 MPH takes about 80 feet (25 m) to stop after the brakes are applied - so perhaps we can estimate that the car/bike combination had a velocity of about 45 MPH immediately after impact - that would account for the car/bike skidding 35m with brakes applied. Using conservation of momentum, that would mean the bike was traveling at (1600+230)/230*45 MPH = 360 MPH at impact. This is clearly a ridiculous answer, but unless you give us more data regarding the coefficient of friction between car and road that's about the only estimate you can make.