Two objects collide head-on (see figure below). The first object is moving with

Question

Two objects collide head-on (see figure below). The first object is moving with an initial speed of v1i = 7.95 m/s and the second object is moving with an initial speed of v2i = 10.00 m/s. Assuming the collision is elastic, m1 = 5.25 kg, and m2 = 6.30 kg, determine the final velocity of each object. (Indicate the direction with the sign of your answer. Positive is to the right, and negative is to the left. Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.)

Explanation / Answer

here,

initial speed of 1 , u1 = - 7.95 m/s

initial speed of 2 , u2 = 10 m/s

m1 = 5.25 kg , m2 = 6.3 kg

let the final velocity of each be v1 and v2

using conservation of momentum

m1*u1 + m2*u2 = m1*v1 + m2*v2

- 5.25 * 7.95 + 6.3 * 10 = 5.25 * v1 + 6.3 * v2 ....(1)

and

using conservation of kinetic energy

0.5 * m1 * u1^2 + 0.5 * m2 * u2^2 = 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2

5.25 * 7.95^2 + 6.3 * 10^2 = 5.25^2 * v1^2 + 6.3 * v2^2 .....(2)

from (1) and (2)

v1 = -4.75 m/s and v2 = 7.34 m/s

or

v1 = 5,86 m/s and v2 = - 1.51 m/s

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