A 1400 kg car is traveling east on the highway at 31 m/s and collides into the rear of a slower moving pickup truck of 2400 kg, which is tra

Question

A 1400 kg car is traveling east on the highway at 31 m/s and collides into the rear of a slower moving pickup truck of 2400 kg, which is traveling east at 25 m/s. Immediately after the collision, the pickup truck is now traveling at 34 m/s to the east. Determine the speed of the car immediately after the collision.

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Hồng Cúc 3 months 2021-08-12T08:11:10+00:00 1 Answers 0 views 0

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    2021-08-12T08:12:37+00:00

    Answer: 31 m/s due east

    Explanation: this question can be solved using the law of conservation of linear momentum.

    This law states that in a closed or isolated system, during collision, the vector sum of momentum before collision equals the vector sum of momentum after collision.

    Momentum = mass × velocity

    From our question, our parameters before collision are given below as

    Mass of car = mc = 1400kg

    Speed of car =vc = 31 m/s (due east)

    Mass of truck = mt = 2400kg

    Velocity of truck = vt = 25 m/s ( due east )

    After collision

    Velocity of car = ?

    Velocity of truck = 34 m/s ( due east )

    Vector sum of momentum before collision is given as

    1400 (31) + 2400 (25) = 43400 + 60000 = 103400 kgm/s

    After collision the truck is seen to move faster (v = 34 m/s) which implies that the car also moves due east .

    1400 (v) + 2400(25) …. A positive value is between both momenta because they are in the same direction.

    After collision, we have that

    1400v + 60000

    Vector sum of momentum before collision = vector sum of momentum after collision

    103400 = 1400v + 60000

    103400 – 60000 = 1400v

    43400 = 1400v

    v = 43400/ 1400

    v = 31 m/s due east

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