Projectile motion
Projectile motion studies motion of objects that are moving upwards or downwards while experiencing a force due to gravity.
Let us start with the equations of motion. We will begin with these equations and their structure
In understanding projectile motion, you need to understand functions in mathematics. Looking at these equations, you see relationship between the variables can be explained using maths functions.
From these equations, you will be expected to draw functions of relationships: position vs. time; velocity vs. time; and acceleration vs. time.
Let's look at (1), it can give us a linear function of position vs. time. Considering our topic, this is not relevant since our motion is under the influence of gravity. We therefore consider (2). It gives a position vs. time relationship which exhibits a parabolic function. The following figures are what your functions should look like:
You will see such a figure when you have chosen your upwards motion as positive. This means your gravitational constants, will be -9.81 m/(s^2). NB: the situation here is that a projectile was thrown vertically up and returns to the initial height/position.
The following is when downwards is chosen as positive.
Now looking at (3). This will give you a linear graph with v_i as a y-intercept. This equation gives the relationship; position vs. time. The gradient of this function is gravitational constant. Now let's look at how the graph looks like.
Velocity vs. time graph when upwards is chosen as positive. The gravitational constant is negative, thus, a negative slope
Velocity vs. time graph when downwards is chosen as positive. The gravitational constant is positive, thus, a positive slope.
Lastly, let's look at acceleration versus time graph. It is worth noting that acceleration is constant for vertical motion. Remember, it is only gravity that's playing part. The graphs are as follows:
In the above, upwards is chosen as positive. We therefore expect the line to be in the negative y-axis.
In the above, downwards is chosen as positive.
We will later cover examples. Stay in touch with Ramta Solutions to get the latest notes. Contact us now to get your tutor and get more information on this.
References:
Mind the gap, Grade 12 Physical Science Study Guide
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