Help please **Problem Description:**An unstable nucleus of mass \(1.7 \times 10^{-26}\) kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. - One particle, having a mass of \(m_1 = 2.6 \times 10^{-27}\) kg, moves in the positive y-direction with speed \(v_1 = 5.6 \times 10^6\) m/s.- Another particle, of mass \(m_2 = 9.0 \times 10^{-27}\) kg, moves in the positive x-direction with speed \(v_2 = 3.4 \times 10^6\) m/s.Find the magnitude and direction of the velocity of the third particle. (Assume that the +x-axis is to the right and the +y-axis is up along the page.)**Solution:**- **Magnitude:** ____ m/s- **Direction:** ____ ° counterclockwise from the +x-axis

Use the conservation of momentum to solve for the velocity of the third particle. pi=pfMv=m1v1+m2v2+m3v3 1 The mass of the third particle can be written as m3=M-m1+m2m3=1.7×10-26kg-2.6×10-27kg+9.0×10-27kgm3=5.4×10-27kg 2 Since the unstable nucleus is initially at rest, the initial momentum is zero. Use the conservation of momentum along the X axis to solve for the velocity of the third particle along the X axis. 0=m1v1x+m2v2x+m3v3x v1x=0v3x=-m2v2xm3v3x=-9.0×10-27kg3.4×106m/s5.4×10-27kgv3x=-5.67×106m/s 3Use the conservation of momentum along the Y axis to solve for the velocity of the third particle along the Y axis. 0=m1v1y+m2v2y+m3v3y v2y=0v3y=-m1v1ym3v3y=-2.6×10-27kg5.6×106m/s5.4×10-27kgv3y=-2.70×106m/s 4 The magnitude of velocity of third particle is as follows: v3=v3x2+v3y2v3=-5.67×106m/s2+-2.70×106m/s2v3=6.28×106m/s 5 The direction of the velocity of the third particle is as follows: θ=tan-1v3yv3xθ=tan-1-2.70×106m/s-5.67×106m/sθ=25.5° 6 The direction of velocity of third particle counter clockwise from the positive X axis is 205.5 degree.

Science

Physics

An unstable nucleus of mass 1.7 x 10-26 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m, = 2.6 x 10-27 kg, moves in the positive y-direction with speed v, = 5.6 x 10° m/s. Another particle, of mass m, = 9.0 x 10-27 kg, moves in the positive x-direction with speed v, = 3.4 x 106 m/s. Find the magnitude and direction the velocity of the third particle. (Assume that the +x-axis is to the right and the +y-axis is up along the page.) magnitude m/s direction ° counterclockwise from the +x-axis

An unstable nucleus of mass 1.7 x 10-26 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m, = 2.6 x 10-27 kg, moves in the positive y-direction with speed v, = 5.6 x 10° m/s. Another particle, of mass m, = 9.0 x 10-27 kg, moves in the positive x-direction with speed v, = 3.4 x 106 m/s. Find the magnitude and direction the velocity of the third particle. (Assume that the +x-axis is to the right and the +y-axis is up along the page.) magnitude m/s direction ° counterclockwise from the +x-axis

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Help please

**Problem Description:**

An unstable nucleus of mass \(1.7 \times 10^{-26}\) kg, initially at rest at the origin of a coordinate system, disintegrates into three particles.

- One particle, having a mass of \(m_1 = 2.6 \times 10^{-27}\) kg, moves in the positive y-direction with speed \(v_1 = 5.6 \times 10^6\) m/s.
- Another particle, of mass \(m_2 = 9.0 \times 10^{-27}\) kg, moves in the positive x-direction with speed \(v_2 = 3.4 \times 10^6\) m/s.

Find the magnitude and direction of the velocity of the third particle. (Assume that the +x-axis is to the right and the +y-axis is up along the page.)

**Solution:**

- **Magnitude:** ____ m/s
- **Direction:** ____ ° counterclockwise from the +x-axis

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