Question

Q- Two cars collided at an intersection their frames became enmeshed and they moved together sd one object. As an accident investigator on the scene determined, Car A has a mass of 1700 kg travelling eastward. Car B had a mass of 2000kg and had an onbord computer that registered a southwards velocity 9.5 m/s. The tire skid marks on the payment showed that they both moved -57 degrees sout east.

1. Velocity in y direction after collision?
2. Magnitude of their total velocity after collision?
3. Velocity in x direction after collision?
4. Car A’s initial velocity before collision?
5. As the speed limit for both sides is 30mph was any car speeding before the collision?

Answer 1

let East be towards +x

let mA = 1700 kg
mB = 2000 kg
vB = -9.5 m/s
theta = 57 degrees

let vx and vy are the component of final velocity of the cars.

Apply conservation of momentum in y-direction

mB*vB = (m1 + m2)*vy

vy = mB*vB/(m1 + m2)

= 2000*(-9.5)/(1700 + 2000)

= -5.14 m/s

|vy| = 5.14 m/s <<<<<<<<<<<-------------------Answer

use, v*sin(57) = vy

v = vy/sin(57)

= 5.14/sin(57)

= 6.13 m/s <<<<<<------------------Answer

vx = v*cos(57)

= 6.13*cos(57)

= 3.34 m/s <<<<<<------------------Answer

Apply conservation of momentum in x-direction

mA*vA = (mA + mB)*vx

vA = (mA + mB)*vx/mA

= (1700 + 2000)*3.34/1700

= 7.23 m/s   <<<<<<------------------Answer

speed limiy, v_limit = 30 mph

= 30*1.609*5/18 m/s

= 13.4 m/s

clearly, vA < v_limit and vB < v_limit

so, no car speeding before the collision.