Question

Practice Problem 8.8 1of1 REFLECT Were you tempted to fr d the final velochy by taki o the vac or sum of the ritial valocitas? If ” ask yourself why you would C pect that to work.b there a la a consevatin cf volactice? Aosa Te, ncr the conserved quanticy is the total momenum of the eyetem. Constants Suppose a small oompact car with amss ol 10Do kg is traveling north on Morewood friction is C 5, te fricton force s about 1 DOOC N.»hich sounds liks a large force. But supposethetruck runs nto ? brick all while going 10 m/s kinetic cnergyjust beore mpact 20 ke 10m/9 2 1.0 1?J 80 the oc» applied by tw wall st do 1.0 × 10. at ^ork on 1 t utk to stop and can 18 it The Ini k may cr r da 0 2 m ar sa tor tha stopping troe to do m/s. It's now 2 seconds ?fer the colision nos occurred Fortunately, all occupants were wearing sest belts and there were no rjuzs, but the two valcies became thoraughly tangled and moved away from the pointof mpactas one mazs. The insurance aduster Part A Practice Problem: atick bogether aiter the colision, find the magniude of the electy of the wreckage. Cxpress your answer In meters per sccond to two signlficant figures. mys Previous Answars Request Answar X Incorrect Try Again Figure Part B Practice Problem: Rafcrring PartA find he drcction of the valocty of the wcckage Exprass your answar in dagneesto rwo signiticant tiguras. Tha angla should ba measured cnuntarclockwisa trom rha+ axis. 2000 kg R Assignment Provide Feedbeck

Suppose a small compact car with a mass of 1000 kg is traveling north on Morewood Avenue at a speed of 15 m/s. At the intersection of Morewood and Fifth Avenues, it collides with a truck with a mass of 2000 kgthat is traveling east on Fifth Avenue at 10 m/s. It’s now 2 seconds after the collision has occurred. Fortunately, all occupants were wearing seat belts and there were no injuries, but the two vehicles became thoroughly tangled and moved away from the point of impact as one mass. The insurance adjuster has asked you to help find the velocity of the wreckage just after impact.

Suppose that just before the collision, the driver of the car swerves, so that the car is still traveling at a speed of 15 m/s, but in the direction of 13? east of north when the car collides with the truck. If the two vehicles stick together after the collision, find the magnitude of the velocity of the wreckage.

Express your answer in meters per second to two significant figures.

Referring to Part A, find the direction of the velocity of the wreckage.

Express your answer in degrees to two significant figures. The angle should be measured counterclockwise from the +x axis.

Answer 1

m1(car) = 1000 kg

v1 = 15*sin13i + 15*cos13 j

m2(truck) = 2000 kg

v2 = 10 i

initial momentum Pi = m1*v1 + m2*v2

after collision

final momentum Pf = (m1+m2)*v

from momentum conservation

Pf = Pi

(m1 + m2)*V = m1*v1 + m2*v2

(1000 + 2000)*V = (1000*15*sin13i )+ (1000*15*cos13j) + (2000*10 i)

3000*V = 3374.26 i + 14615.55 j + 20000 j

V = 7.79 i + 4.87 j

magnitude = sqrt(7.79^2+4.87^2) = 9.2 m/s

part(B)

direction = tan^-1(4.87/7.79) = 32 degrees east of north