Kinematics of a Particle: Curvilinear Motion

In summary, a radar is tracking a rocket and at some instant of time, the distance r is measured as 10 mi and angle 30º. The velocity and acceleration of the rocket can be determined using the relationships between displacement, velocity, and acceleration, as well as the concepts of absolute circular motion and angular velocity and acceleration. The derivatives of r are 650 ft/s and 165 ft/s^2, and the derivatives of the angle 30º are estimated to be 0.031 rad/s and 0.005 rad/s^2. The velocity is calculated to be 1761 ft/s using the formula for velocity, and the acceleration is 325 ft/s^2.
  • #1
rcbq36
2
0
A radar is tracking a rocket. At some instant of time, the distance, r measured as 10 mi and angle 30º. Determine the velocity and
acceleration of the rocket.

Velocity: v = ds/dt, Acceleration: a=dv/dt
Relationship Displacement- velocity –acceleration: ads = vdv
Absolute Circular Motion- Angular Velocity: ω =dθ/dt
Angular Acceleration: α= dω/dt= d^2θ/dt^2
Relationship Displacement - Velocity – Acceleration: ωdω = αdθ

Ok I know that the derivatives of r are: 650 ft/s , 165 ft/s^2 , and the derivates of the angle 30º are estimated to be: 0.031 rad/s, and 0.005 rad/s^2. That is all the info I have. I converted the 10 mi= 52,800 ft. And the professor gave us the answers: the velocity is supposed to be: 1761 ft/s and the acceleration 325 ft/s^2 I just don't know how to get there.
 
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  • #2
Never mind. I was looking at the wrong formulas. This is the one:
velocity= square rootof of[650^2+(52,800)(0.031)^2]=1761 ft/s
 

Related to Kinematics of a Particle: Curvilinear Motion

1. What is curvilinear motion?

Curvilinear motion is the motion of an object along a curved path. This means that the object is changing direction as it moves, and its velocity and acceleration are not constant.

2. How is curvilinear motion different from linear motion?

Curvilinear motion differs from linear motion in that the path of the object is not a straight line. In linear motion, the object moves along a straight line and its velocity and acceleration are constant. In curvilinear motion, the object's velocity and acceleration are constantly changing due to the changing direction of its motion.

3. What is the equation for displacement in curvilinear motion?

The equation for displacement in curvilinear motion is s = ∫v dt, where s is the displacement, v is the velocity, and t is the time interval. This equation is used to calculate the total distance traveled along a curved path.

4. How is acceleration calculated in curvilinear motion?

Acceleration in curvilinear motion is calculated using the equation a = dv/dt, where a is the acceleration, v is the velocity, and t is the time interval. This equation takes into account the constantly changing velocity and direction of the object to determine its acceleration.

5. What are some real-life examples of curvilinear motion?

Some real-life examples of curvilinear motion include a rollercoaster moving along its track, a ball being thrown in a curved path, and a car making a turn on a curved road. These examples all involve an object moving along a curved path and changing direction, making them examples of curvilinear motion.

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