To determine the average horizontal and vertical velocities of a pendulum, we need to consider its motion in terms of angular velocity and the given parameters.
The horizontal velocity component (Vx) of a pendulum is zero because the motion occurs only in the vertical plane. The vertical velocity component (Vy) changes as the pendulum swings back and forth. At the highest point of the swing, the vertical velocity is maximum, while at the lowest point, it is zero.
To find the average vertical velocity, we can calculate the initial and final vertical velocities and average them.
Given: Length of the pendulum (r) = 1 m Angle of swing (theta) = 15 degrees
To calculate the initial vertical velocity (Vyi), we need to determine the vertical component of the initial velocity at the highest point of the swing. At this point, the entire initial velocity is directed vertically.
Vyi = V_initial * sin(theta)
The initial velocity (V_initial) is the velocity when the pendulum is released from its initial position. Since no initial velocity is given in the question, we assume it to be zero. Thus, V_initial = 0.
Vyi = 0 * sin(theta) = 0
The final vertical velocity (Vyf) occurs when the pendulum reaches the lowest point of the swing. At this point, the entire velocity is horizontal, and there is no vertical component. Hence, Vyf = 0.
The average vertical velocity (Vy_avg) is then the average of the initial and final vertical velocities:
Vy_avg = (Vyi + Vyf) / 2 = (0 + 0) / 2 = 0 / 2 = 0
Therefore, the average vertical velocity of the pendulum is 0 m/s.
In summary: Average horizontal velocity (Vx) = 0 m/s Average vertical velocity (Vy) = 0 m/s