An unstable nucleus with a mass of 18.0 ✕ 10-27 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.0 ✕ 10-27 kg, moves along the positive y-axis with a speed of 9.0 ✕ 106 m/s. Another particle, of mass 7.4 ✕ 10-27 kg, moves along the positive x-axis with a speed of 1.0 ✕ 106 m/s. (Assume that mass is conserved.)
What is the direction of motion?
in ° (from the positive x-axis)
the momentum components of the third particle will be eequal and opposite the components of the other two particles.
so the velocity components will be
V=x</b)(-7.4E-27/mass3 +y(-0E6)/5E-27)/mass3
where mass3 the mass of the third particle is 18E-27-5E27-7.4E-27
To find the direction of motion in degrees (from the positive x-axis), we can use trigonometry.
First, let's identify the components of motion for each particle:
Particle 1:
Mass (m1) = 5.0 ✕ 10^(-27) kg
Speed (v1) = 9.0 ✕ 10^6 m/s
Direction: Along the positive y-axis (vertical direction)
Particle 2:
Mass (m2) = 7.4 ✕ 10^(-27) kg
Speed (v2) = 1.0 ✕ 10^6 m/s
Direction: Along the positive x-axis (horizontal direction)
Now, we can calculate the angle θ (from the positive x-axis) using the tangent function:
θ = arctan(v1/v2)
Substituting the values:
θ = arctan((9.0 ✕ 10^6 m/s) / (1.0 ✕ 10^6 m/s))
Using a calculator or trigonometric table, we find:
θ ≈ 81.87°
Therefore, the direction of motion is approximately 81.87° from the positive x-axis.