# Multiflash photographs of projectiles

##### Demonstration

More evidence of Galileo’s insight: that horizontal and vertical motions of a projectile are independent of each other.

#### Apparatus and materials

Steel ball (2.5 cm in diameter is ideal)

Camera and multiflash system

Retort stand and boss

Lamp, 500 W

#### Health & Safety and Technical notes

Read the Guidance note Multiflash Photography for detail of specific methods and for general hints.

You will need a grid made of equally spaced horizontal and vertical lines. Position this so that it is in the background when the camera operates.

A different experiment shows this insight too: Monkey and Hunter, with a video of it freely available from the National STEM Centre eLibrary.

#### Procedure

Making the image
a
Set up the multiflash system.

b Start the camera and multiflash system and then launch the ball by rolling it along the bench, so that it rolls off.

Analyzing the image
c Use the horizontal and vertical scales to compare the horizontal and vertical spacings of the ball images.

d Describe what happens to the horizontal spacings between each position of the ball.

e Describe how the vertical spacings change.

#### Teaching notes

1 Students should see that the horizontal spacings are constant, since the horizontal velocity is constant. They should see that the vertical spacings increase according to s=1/2 at2, since the vertical velocity increases as the ball accelerates downwards.

The two motions have different causes and behave differently. It is valid and useful to consider them separately.

Galileo realized this and used the idea to analyze cannonball motion. This revolutionized ‘ballistics’ and hence warfare.

2 You could repeat this using a ball showing:

• vertical motion of a ball bearing
• horizontal motion along a bench at constant speed
• projectile motion of a ball bearing thrown out horizontally
• two ball bearings released simultaneously; one to perform vertical motion and the other thrown horizontally to follow parabolic projectile motion.

3 Analyze the photographs by transferring the motion to an overlaid grid (e.g. a sheet of acetate). Mark the positions of the ball bearing on the sheet and then draw lines horizontally and vertically through the ball bearing positions.

Check the vertical motion for constant acceleration (the horizontal lines are spaced from the top in intervals of 1:4:9:16 ...). Check the horizontal motion for constant speed (the vertical lines are equally spaced).

To calculate the acceleration due to gravity: measure the average speed of the ball bearing near to the beginning of its motion and near to the end. Divide the time taken between these two calculations, i.e. from the centre of the space between the two positions of the ball bearing for which the average speed was calculated in the first position. (It will be the time for one less flash than the number of images between the first ball position measured and the last.)

This experiment was safety-checked in March 2005