A projectile proton with a speed of 1100 m/s collides elastically with a target proton initially at rest. The two protons then move along pe

Question

A projectile proton with a speed of 1100 m/s collides elastically with a target proton initially at rest. The two protons then move along perpendicular paths, with the projectile path at 45° from the original direction. After the collision, what are the speeds of (a) the target proton and (b) the projectile proton?

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Thanh Thu 3 years 2021-07-31T15:37:34+00:00 1 Answers 13 views 0

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  1. linhdan
    0
    2021-07-31T15:38:43+00:00
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    Answer:

    So, the target proton’s speed is  777.82 m/s

    And, the projectile proton’s speed is  777.82 m/s

    Explanation:

    as per the system, it conserves the linear momentum,

    so along x axis :

    Mp V1 (i) = Mp V1 (f) cos θ1 + Mp V2 (f) cos θ2

    along y axis :

    0 = -Mp V1 (f) sin θ1 + Mp V2 (f) sin θ2

    let us assume before collision it was moving on positive x axis, hence target angle will be θ2 = 45° from x axis

    V2(f) = V1 (i) sin θ1 / ( cosθ2 sin θ1 + cos θ1 sin θ2)

          =  1100 * sin 45 / ( cos 45 sin 45 + cos 45 sin 45 )

         =  1100 * 0.7071 /( 0.7071 * 0.7071 +0 .7071 * 0.7071 )

         = 777.82 /( 0.5 + 0.5)

        = 777.82 m/s

    (b) 

     the speed of projectile , V1 (f) = sinθ2 * V2(f) / sinθ1

                                                                  = sin 45 * 777.82 / sin 45

                                                                  = 777.82 m/s

    So, the target proton’s speed is  777.82 m/s

    And, the projectile proton’s speed is  777.82 m/s

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