Resource: Projectile Motion

Print Background Essay

Imagine you were to drop a rock over the edge of a cliff and wanted to describe the motion of the falling rock. When describing the motion of a falling object, you need to address several factors, such as its position (i.e., location), speed, and direction of motion. Assuming that the cliff has a sheer face and that you were careful not to apply any initial force, the rock would follow a vertical path straight towards the ground. As each second passed, the rock would fall farther away from you and closer to the ground below.

If you could measure the distance that the rock falls each second, you would see that it falls at a faster rate as time goes on—in other words, it accelerates. This happens because gravity is affecting the motion of the rock. On Earth, the acceleration due to gravity is about 9.8 m/s². That is, with every second that passes, the downward velocity of the rock increases by about 9.8 m/s. Velocity is the speed of an object in a given direction.

Now imagine that you were to throw the rock so that it was launched horizontally from the edge of the cliff. How would you describe the motion of the rock in this scenario?

In this case, the rock would travel a curved path because it has two components of motion: horizontally away from the cliff, as well as vertically toward the ground. The force of the launch projects the rock with a horizontal velocity. If no other forces act on the rock, it will continue to travel horizontally at a constant velocity. However, the rock is also accelerated downward by gravity, just as it was in the dropped-rock scenario. Though independent of each other (the vertical force does not affect the horizontal velocity), the horizontal and vertical motions create a curved trajectory, or path of motion, when they are combined.

This type of motion is called projectile motion. Neglecting the effects of air resistance, a projectile travels through space with only the force of gravity acting on it. Thus, a projectile has a constant horizontal velocity and a constant downward vertical acceleration. Because the acceleration due to gravity is the same for all objects, in the absence of air resistance, objects projected under the same initial conditions (speed, direction, and location of the launch) will travel the same trajectory, regardless of shape, size, or mass. The two-dimensional motion that it traces is a particular type of curve called a parabola.

To learn about a medieval throwing machine, check out Energy Transfer in a Trebuchet.

To learn more about the motion of objects, check out Galileo: His Experiments.

To learn more about Galileo and his studies of motion, check out Galileo: His Place in Science.

Print Questions for Discussion

• In the absence of air resistance, what effect does the mass of a projectile have on its trajectory?
• Compare the horizontal distance the object travels in the first second with the horizontal distance it travels in the second second.
• Can you find evidence that the vertical velocity changes over time?
• What and where are the forces that cause motion in the vertical and horizontal directions? What forces are acting at time t=0? at a point on the way up? at the top of the trajectory? at a point on the way down?