NameClassDate assignedDue Date

Range of a Projectile

Procedure

Purpose: Predict where a horizontally projected object will land

Concept Skill & Check:

If an object moves in only one dimension, it is easy to describe the location of that object and to predict its final position when it comes to rest. On a calm day, an apple falls vertically from a tree limb to the ground below. However, a golf ball hit from the tee, a football thrown over the defensive line to a downfield receiver, and bullets fired from a gun move in two dimensions. Such objects, called projectiles, have horizontal and vertical components of motion that are independent of each other. The independence of vertical and horizontal motion is used to determine the location and the time of fall of projected objects. All projectiles described above had an initial vertical velocity at an angle above the horizontal. To simplify analysis of the motion of the projectile in this experiment, the steel ball will be launched horizontally; therefore, the initial vertical velocity, vy, will be zero.

If you know the velocity, vx, of a ball launched horizontally from a table and the ball’s initial height, y, above the floor, the equation of projectile motion can be used to predict where the ball will land. Recall that the horizontal displacement or range, x of an object with horizontal velocity, vx, at time, t is

The equation describing vertical displacement is that of a body falling with constant acceleration:

But if vy = 0, then

The ball’s fall time can be computed from the equation for vertical motion by solving for t.

The range of the projectile, x, can then be computed. In this experiment, you will try to predict the range of a projectile launched with a certain horizontal velocity.

Materials:

Ring stand/ringv-track or tubeballmasking tape

Book or other objects to make a channelstop watchmeter stickbeaker

Procedure:

  1. Set up the apparatus as shown in the figure. Construct horizontal and inclined ramps on the table top, using the track, ringstand, ring, and masking tape. It must be perpendicular to the edge of the table.Use books to form a channel from the end of the ramp to the edge of the table. Make a few test rolls, but catch the ball as it rolls off the table. The ball should stay in the track when you roll it down the inclined ramp. If the ball jumps out of the ramp, lower the support clamp and try again.
  1. Select a point on the incline where you will release the ball. Mark this spot with a small piece of tape.
  1. With the stopwatch ready to go, release the ball from the tape mark on the ramp. Record the time it takes for the ball to roll through the horizontal channel. Catch the ball as it rolls off the table. Repeat several times until you can get consistent results, releasing the ball from the same place each time. Record the average time in the data table.
  1. At the edge of the table, use the meter stick to mark a place on the floor directly below the point where the ball leaves the table. Hold the meter stick flat against the table edge to be sure it is straight vertically. Put a small piece of tape where the meter stick touches the floor.Measure the vertical distance from the table top to the floor. Record this distance, y, on the data sheet.

Range of a Projectile

Observations & Data

Average time in horizontal channel, t:

Distance of horizontal channel d:

Formula for calculating velocity:

Vertical distance, y:

Formula for vertical distance of an object launched horizontally with constant acceleration:

Formula for horizontal distance of an object launched horizontally:

Analysis:

  1. Compute the horizontal velocity in the channel, vx.
  1. Calculate time, t, that the ball will be falling from the table, using your value for y. (Notice, this is vertical time, not the same as horizontal time calculated in #1.)
  1. Calculate the horizontal distance, x, that the ball should travel, using your values for vx and t. (This time use the same time as in #2 because the length of time the ball is in the air is the same for both its vertical and its horizontal motion.)

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  1. Measure the distance, x, in a straight line from the horizontal channel, starting where the tape is on the floor. Place another small piece of tape at this location. Call the teacher to watch. Place the beakeron the second piece of tape. Mentally account for the height of the beaker and position accordingly. Roll the ball from the same height on the inclined ramp from which it was released earlier. This time, let the ball roll off the table. Did it land in the beaker?If not by more than 5cm, recalculate. If not by less than 5cm you may make a MINOR adjustments in the beaker’s location.
  1. If you were off by a few centimeters, where could the error have come from? Be specific! (“human error” by itself doesn’t cut it.)
  1. Does this experiment support the premise that the horizontal and vertical components of motion are not affected by each other? Explain.
  1. If a very light, but fairly large, sponge ball, or a ping-pong ball, were rolled down the ramp would you expect the same result in the real world? Explain.
  1. Why don’t you need the mass of the ball?

Application

A diver achieves a horizontal velocity of 3.75 m/s from a diving platform located 6.0 m above the

water. How far from the edge of the platform will the diver be when she hits the water?

Extension

Find the horizontal range of a baseball that leaves the bat at an angle of 63° with the horizontal with

an initial velocity of 160 km/h. Disregard air resistance. Show all of your calculations.