A rocket-powered hockey puck is moving on a (friction-less) horizontal air-hockey table. The x- and y-components of its velocity as a function of time are presented in the graphs below. Assuming that at t=0 the puck is at (X0,Y0)=(1,2),
draw a detailed graph of the trajectory y(x).
Do not see graph.
To draw the detailed graph of the trajectory y(x) for the rocket-powered hockey puck, we need to analyze the given x- and y-components of its velocity as a function of time.
Let's start by understanding the information given in the graphs. The x-component of velocity is given as a function of time, which means it shows how the horizontal velocity of the puck changes over time. The y-component of velocity also shows how the vertical velocity of the puck changes with time.
To find the trajectory y(x), we need to integrate the y-velocity with respect to time to obtain the displacement in the y-direction. Since the y-component of velocity is given as a function of time, we can use the area under the y-velocity vs. time graph to calculate the displacement in the y-direction.
Here are the steps to obtain the graph of the trajectory y(x):
1. Start with the given x- and y-components of velocity as a function of time graphs.
2. Integrate the y-velocity with respect to time to obtain the displacement in the y-direction.
3. Choose a time interval and calculate the y-displacement for each interval by finding the area under the y-velocity curve within that interval.
4. Plot the obtained y-displacement values against their corresponding x-values.
5. Connect the plotted points to obtain a smooth curve representing the trajectory y(x).
Note: Since the x-component of velocity is not given, we cannot directly determine the displacement in the x-direction. Therefore, we can only plot the trajectory based on the information provided.
It's important to note that without more information about the x-component of velocity, such as its value or a graph showing its behavior, we cannot accurately determine the complete trajectory of the puck. However, if we assume that the x-component of velocity remains constant throughout, we can use the given information about the y-component of velocity to draw a possible trajectory y(x) graph.
Please provide specific values or more information about the x-component of velocity to further analyze the problem and accurately determine the trajectory of the puck.