Simple Determination of Initial Velocity of a Pojectile

[Chrishaum]

Simple Determination of Initial Velocity of a Projectile

It is possible to roughly determine the initial velocity of a projectile shot from a launcher like the one linked to below using a number of methods.

http://www.science4schools.co.uk/acatalog/10-1365.jpg

Two of which I am aware are:

(1) shooting the projectile horizontally and using the range to calculate the initial velocity and

(2) catching the projectile in a foam block (free to swing) immediately after it is fired and using the change in height to calculate the initial velocity with conservation of energy and momentum. Here is the swinging catcher: http://www.science4schools.co.uk/acatalog/10-1368.jpg

The first method seems to be more accurate, but it takes longer than the second method.

What fast, accurate methods are there for determining the initial velocity, utilizing common physics classroom tools?

 

[NateTG]

Actually, you're not guaranteed that the projectile will stop moving -- it could, for example, go into orbit. You need to keep track of the path to use this method in general.

A method that would work is to keep track of the recoil.

Two gates at a known distance apart is fairily popular and effective.

Alternatively, a strobe light and a camera would give you two locations separated by a known amount of time.

A more sophistcated approach would be to use sound and measure the reflected doppler shift.

 

[Chrishaum]

Thank you for your responses, NateTG.

My end goal in determining the initial velocity is to utilize it in repudiating the following equation for projectile motion:$$y = (tan \theta_0)x - \frac{gx^2}{2(v_0 cos \theta_0)^2}$$

As my experiment stands, a digital camera will capture the trajectory of the ball in a rapid series of photographs. A backdrop behind the path will be marked with a scale and horizontal and vertical axes (with the tip of the projectile launcher being the origin). I will then be able to use an imaging program to find the ball's x- and y-values along the path.

Following your suggestion, I will place two photogates near the origin to find the initial velocity. I thought about finding the distance the ball travels between the first two frames and dividing by the time between the camera's shots. However, this would be less accurate than using the photogate method.