Final answer:
To find the angle between the x-axis and the direction of motion of the two masses after the collision, we can use the principles of conservation of momentum and trigonometry. Using conservation of momentum, we find that the final velocity of the two masses is approximately 3.53 m/s. Then, using trigonometry, we calculate the angle to be approximately 55.0 degrees.
Step-by-step explanation:
Before we find the angle, let's first determine the final velocity of the two masses after the collision. Since mass m1 and m2 stick together, we can use the principle of conservation of momentum to find this final velocity. Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
Before the collision: momentum of m1 = m1 * v1i = 1.2 kg * 2.5 m/s = 3 kg*m/s
momentum of m2 = m2 * v2i = 2.6 kg * 4 m/s = 10.4 kg*m/s
Total momentum before the collision = 3 kg*m/s + 10.4 kg*m/s = 13.4 kg*m/s
After the collision: total momentum = (m1 + m2) * vf
Since m1 and m2 stick together, we can write:
(1.2 kg + 2.6 kg) * vf = 13.4 kg*m/s
3.8 kg * vf = 13.4 kg*m/s
vf = 13.4 kg*m/s รท 3.8 kg = 3.53 m/s
Now, to find the angle, we can use trigonometry. The angle, q, is given by:
tan(q) = opposite/adjacent = vf/v1i
tan(q) = 3.53 m/s / 2.5 m/s
q = arctan(3.53/2.5) = arctan(1.412) = 55.0 degrees
Therefore, the angle between the x-axis and the direction of motion of the two masses after the collision is approximately 55.0 degrees.