For a question in physics... I was told to draw a graph of vertical displacement, y, versus time, t, in 2sec increments from 0 to 1.8. What was given to me was:
v_yo_= +10m/s
v_xo_= +5m/s
a_y_ = -10m/s^2
So I used the formula: y=vo+1/2at^2
I drew the graph, and got a parabala.
Now, my question is, how do I find instantaneous vertical velocity at 6s using the graph?
Do I use the linear question for horizontal motion at all in this problem? x=vo(t)
Any help would be great. THanks
To use the graph only, you could either (1) measure the tangent to the y(t) curve at = 6 s, or (with less accuracy):
(2) divide the difference in y altitudes at t = 7 s and t = 5s by the interval, 2 s.
You could also get the exact answer by differentiating the y(t) function itself, to get Vy (t), but they don't seem to want you to do that.
You will not need the horizontal equation of motion to do this problem.
Alright, thanks. I drew a tangent line and found the slope at t=6, and got 3.75 m/s as my instantaneous velocity.
Just so I know... when do I have to take into consideration the linear equation governing horizonatal motion?
To find the instantaneous vertical velocity at 6 seconds using the graph you drew, you can follow these steps:
Step 1: Identify the point on the graph that represents 6 seconds on the x-axis.
Step 2: Read the corresponding value on the y-axis. This represents the vertical displacement at 6 seconds.
Step 3: Calculate the slope of the tangent line at that point. The slope of the tangent line represents the instantaneous vertical velocity at that specific instance.
Now, let's answer your second question. In this problem, since you are dealing with vertical motion (y-coordinate), you do not need to use the linear equation for horizontal motion (x-coordinate). The horizontal motion is not directly involved in finding vertical displacement or velocity.
Remember that horizontal motion and vertical motion are separate components and can be treated independently if there is no interaction between them.
I hope this clarifies how to find the instantaneous vertical velocity and the relevance of the horizontal motion equation in this problem.