Basic equations needed for your answers: PLEASE DRAW A DIAGRAM AS WELL P = M x V

Question

Basic equations needed for your answers: PLEASE DRAW A DIAGRAM AS WELL

P = M x V 1 mile =1609 meters

M1V1x + M2V2x = M1V1x + M2V2x M1V1x + M2V2x = M1V1x + M2V2x

a. A 1500.0 kg car is travelling due west at 60.0 mph. A 2,000 kg pickup truck is travelling SW (45 deg) at 70 mph on an intersecting road. The pickup truck does not stop for the stop sign and impacts the car in an inelastic collision. What is their resultant velocity?

b. A 0.17 kg cue ball, moving at 2.5 m/s, hits a stationary billiards ball (0.16 kg) at an angle, causing the billiards ball to travel 35 degrees to the left, and the cue ball, 55 degrees to the right. What are their resultant velocities?

Explanation / Answer

m1 = 1500 kg            m2 = 2000 kg

v1i = -60 mph i                 v2i = -70*cos45i - 70*sin45j

momentum before collision

Pi = m1*v1i + m2*v2i

after collision

v1f = v2f = v

momentum after collision

Pf = (m1+m2)*v

from momentum cosnervation

Pf =Pi

(1500+2000)*v = -(1500*60)i - (2000*70*cos45)i - (2000*70*sin45)j

V = -54 i - 28.3 j

magnitude = sqrt(54^2+28.3^2) = 61 mph = 61*1609/(3600) = 27.3 m/s

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part(b)

along horizontal

0.17*2.5 = 0.17*v1*cos55 + 0.16*v2*cos35

0.425 = 0.098*v1 + 0.13*v2 .......(1)

along vertical

0 = -0.17*v1*sin55 + 0.16*v2*cos35

0 = -0.14*V1 + 0.13*v2.........(2)

v2 = 1.1*v1

KEi = KEf

(1/2)*0.17*2.5^2 = (1/2)*0.17*v1^2 + 0.16*v2^2

(1/2)*0.17*2.5^2 = (1/2)*0.17*v1^2 + 0.16*(1.1*v1)^2

v1 = 1.38 m/s <<<<--------answer

v2 = 1.1*v1 = 1.52 m/s <<<------answer

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