How to Calculate Impact Distance in Ballistic Motion with Given Energy?

[sheri1987]

Homework Statement

The start point of a ballistic launcer is h1 = 18 cm above its launch point (including the correction for the starting angle) and the launch point is h2 = 35 cm above the bench top. A steel ball rolled down the launcher has a mass of 10.2 g. Answer the following question:


Calculate the impact distance when UNC = 0.00216 J. Express your answer in cm

Homework Equations

l^2 = ((20/7)(h1-(UNC/mg))h2
l = impact distance
g= gravity 9.81
m= 10.2 g
h1 = 18 cm
h2 = 35 cm
UNC = given

The Attempt at a Solution

I plugged in the numbers and solved for l (impact distance) and got ) 42.43 cm, but for some reason the computer program I am plugging it into says its wrong. Can you help me out please? Thanks!

 

[loonychune]

I don't get 42.43 cm, though I get something similar when i start leaving the units in the form they're in.

Mass is given in grams and h1 and h2 in cm.. convert all to SI units and then back to cm. The formula is a wee bit more complicated than need be... since 35cm = 0.35m = 7/20 you only need worry about h1 - (UNC/mg) = l^2

If this is your only concern then i hope this sorts things out... I'm not quite sure i understand the problem myself but as far as plugging numbers into that formula there seems to definitely be some issues with units...

 

[baba89]

There are a few things that could be causing the discrepancy between your answer and the computer's answer. First, make sure you are using the correct units for all your values. In this case, it looks like all the units are in centimeters and grams, so make sure you are not accidentally using meters or kilograms. Additionally, make sure you are using the correct value for g (9.81 m/s^2 or 981 cm/s^2).

Also, check your calculations to make sure you are using the correct order of operations and that you are not rounding any values too early. Sometimes, small rounding errors can accumulate and result in a slightly different answer.

If you are still having trouble, try double checking the formula you are using to make sure you are using the correct one for this specific problem. It may also be helpful to double check your work with a classmate or a teacher to see if they get the same answer.

Overall, it's important to carefully follow the given equations and make sure all units and values are correct in order to arrive at the correct answer. Good luck!