Particle Motion in the y-z Plane: Velocity and Acceleration

At t = 0.7 seconds:

1. What is the velocity in the y-direction?

2. What is the velocity in the z-direction?

3. What is the acceleration in the y-direction?

4. What is the acceleration in the z-direction?

5. What is the magnitude of the velocity?

6. What is the angle of the velocity vector with respect to the y axis?

Answers:

1. The velocity in the y-direction at t = 0.7 seconds is 21.504 m/s.

2. The velocity in the z-direction at t = 0.7 seconds is -6.533 m/s.

3. The acceleration in the y-direction at t = 0.7 seconds is 36.066 m/s².

4. The acceleration in the z-direction at t = 0.7 seconds is -10.458 m/s².

5. The magnitude of the velocity at t = 0.7 seconds is 22.548 m/s.

6. The angle of the velocity vector with respect to the y axis is approximately 16.614 degrees.

To find the velocity in the y-direction, we take the derivative of the y equation with respect to time. Similarly, the velocity in the z-direction is obtained by differentiating the z equation with respect to time. Substituting t = 0.7 seconds into these derivatives gives the respective velocities.

For the acceleration in the y-direction, we differentiate the velocity equation in the y-direction with respect to time. Similarly, the acceleration in the z-direction is obtained by differentiating the velocity equation in the z-direction with respect to time. Substituting t = 0.7 seconds into these derivatives gives the respective accelerations.

Understanding the motion of particles in different directions and their velocities and accelerations can provide valuable insights into the dynamics of the system. It helps in predicting the behavior of the particle at different time intervals and analyzing its trajectory.