Kinetic Energy:

$\overline{)\begin{array}{rcl}\mathbf{K}\mathbf{.}\mathbf{E}& {\mathbf{=}}& \frac{\mathbf{1}}{\mathbf{2}}{\mathbf{mv}}^{\mathbf{2}}\end{array}}$

The kinetic energy of an object is directly proportional to the mass of the object.

To understand how the trajectory of an object depends on its initial velocity, and to understand how air resistance affects the trajectory. For this problem, use the PhET simulation Projectile Motion. This simulation allows you to fire an object from a cannon, see its trajectory, and measure its range and hang time (the amount of time in the air). Click to launch video simulation Start the simulation. Press Fire to launch an object. You can choose the object by clicking on one of the objects in the scroll-down menu at top right (a cannonball is not among the choices). To adjust the cannon barrel’s angle, click and drag on it or type in a numerical value (in degrees). You can also adjust the speed, mass, and diameter of the object by typing in values. Clicking Air Resistance displays settings for (1) the drag coefficient and (2) the altitude (which controls the air density). For this tutorial, we will use an altitude of zero (sea level) and let the drag coefficient be automatically set when the object is chosen. Play around with the simulation. When you are done, click Erase and select a baseball prior to beginning Part A. Leave Air Resistance unchecked.

You might think that it is never a good approximation to ignore air resistance. However, often it is. Fire the baseball without air resistance, and then fire it with air resistance (same angle and initial speed). Then, adjust the mass of the baseball (increase it and decrease it) and see what happens to the trajectory. Don’t change the diameter. When does the range with air resistance approach the range without air resistance?

- It never does. Regardless of the mass, the range with air resistance is always shorter than the range without.
- The range with air resistance approaches the range without air resistance as the mass of the baseball decreases.
- The range with air resistance approaches the range without air resistance as the mass of the baseball increases.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Solving Projectile Motion Using Energy concept. You can view video lessons to learn Solving Projectile Motion Using Energy. Or if you need more Solving Projectile Motion Using Energy practice, you can also practice Solving Projectile Motion Using Energy practice problems.