A particle is traveling with a constant radial velocity of 12 ft/s. The transver

Question

A particle is traveling with a constant radial velocity of 12 ft/s. The transverse component of its velocity is constant at 7 ft/s. At a time of t = 10 seconds (particle starts from rest) with the particle located 30 feet from the origin of a Cartesian system, the transverse unit vector makes an angle of 225 degrees, counterclockwise with the horizontal, positive x axis. Using rotation matrices determine:

1. The velocity of the particle in the Cartesian coordinate system

2. The acceleration of the particle in the Cartesian coordinate system

3. If the tangent to the trajectory of the particle at t = 10 seconds makes an angle of 25 degrees, counterclockwise with the transverse unit vector, determine velocity and acceleration in the normal-tangential coordinate system.

4. Determine radius of curvature of the trajectory at t = 10 seconds.

Explanation / Answer

[1] V= Vxi+Vyj= [12i+7j] ft/s

[2] a= [axi+ayj ] = [ 1.2 i+0.7 j ] ft/s2

[3] Vy= 7*sin theta= 7*sin [250] = 2.96 ft/s

ay= 7*sin theta= 0.7*sin [250] = 0.296 ft/ s2

[4] r= [ rxi+ryj ] = [ 30*cos [225o] i +30 *sin [225o] j ] = [ -21.21 i - 21.21 j] ft

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.