Answered: Two cars collide at an icy intersection…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1400 kg and was approaching at 4.00 m/s due south. The second car has a mass of 750 kg and was approaching at 23.0 m/s due west.(a) Calculate the final velocity of the cars. (Note that since both cars have an initial velocity, you cannot use the equations for conservation of momentum along the x-axis and y-axis; instead, you must look for other simplifying aspects..)
Magnitude

Direction
(counterclockwise from west is positive)

(b) How much kinetic energy is lost in the collision? (This energy goes into deformation of the cars.)

Expert Solution

Step 1

$Solution : According to the conservation of momentum we have : The momentum in west direction to be : m_{1} v_{1} + m_{2} v_{2} = (m_{1} + m_{2}) v_{x} Applying values we get : (1400 \times 0) + (750 \times 23) = (1400 + 750) v_{x} \Rightarrow v_{x} = \frac{(750 \times 23)}{(1400 + 750)} \Rightarrow v_{x} = \frac{17250}{2150} \Rightarrow v_{x} = 8.023 m / s The momentum in south direction will be : m_{1} v_{1} + m_{2} v_{2} = (m_{1} + m_{2}) v_{y} Applying values we get : (1400 \times 4) + (750 \times 0) = (1400 + 750) v_{y} \Rightarrow v_{y} = \frac{(1400 \times 4)}{(1400 + 750)} \Rightarrow v_{y} = 2.605 m / s Magnitude of final velocity will be given as : v = \sqrt{v_{x}^{2} + v_{y}^{2}} = \sqrt{{(8.023 m / s)}^{2} + {(2.605 m / s)}^{2}} = 8.4353 m / s The direction of velocity will be : θ = \tan^{- 1} (\frac{v_{y}}{v_{x}}) \Rightarrow θ = \tan^{- 1} (\frac{2.605 m / s}{8.023 m / s}) = 17.988 ° \approx 18 °$