Calculating Impact Speed of 4.00kg Cannon Ball Dropped from 55.0m

In summary, using energy conservation and assuming negligible air resistance, the impact speed of a 4.00 kg cannon ball dropped from a height of 55.0 m can be calculated by setting potential energy equal to kinetic energy and solving for the speed, resulting in an impact speed of approximately 33 m/s.
  • #1
redbutterfly
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Homework Statement


Using energy conservation and assuming negligible air resistance, calculate the impact speed of a 4.00 kg cannon ball after being dropped from a height of 55.0 m.



Homework Equations


KE sub total=KE sub 1+KE sub 2
speed=distance/time
gravity=9.8


The Attempt at a Solution


I'm completely lost as to how to get this with energy conservation. Can someone please help?
 
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  • #2
Welcome to the physics forums! Hope you ask lots of questions here.

As the ball drops, its gravitational potential energy is converted to kinetic energy. Start with:
Potential energy at the top = kinetic energy at the bottom

Fill in the detailed formulas, solve for the quantity you want to find, then put in the numbers you know.
 
  • #3
Thank you!

TE=KE+PE sub g
PE sub g=mgh
PE sub g=4*9.8*55=2200 J
KE=0
TE=0+2200
2200=KE+0
KE=2200=1/2*4*v^2
4400=4*v^2
1100=v^2
v=33 m/s
 
  • #4
That's it!
Maybe simpler to write mgh = 1/2m*v^2, cancel the m's, then solve for v:
v = sqrt(2gh) = sqrt(2*g*55) = 32.8 m/s
 

FAQ: Calculating Impact Speed of 4.00kg Cannon Ball Dropped from 55.0m

1. How do I calculate the impact speed of a 4.00kg cannon ball dropped from 55.0m?

To calculate the impact speed of a 4.00kg cannon ball dropped from 55.0m, you can use the equation v = √(2gh), where v is the impact speed, g is the acceleration due to gravity (9.8m/s²), and h is the height from which the ball was dropped (in this case, 55.0m).

2. What units should I use for the calculation?

For the calculation, you should use meters for distance and seconds for time. This will result in the impact speed being measured in meters per second (m/s).

3. Can I use this equation for any object dropped from a height?

Yes, this equation can be used for any object being dropped from a height, as long as the object is dropped in a vacuum or the air resistance is negligible. This is because the equation assumes that the only force acting on the object is gravity.

4. Are there any other factors that can affect the impact speed?

Yes, there are other factors that can affect the impact speed of a dropped object. These include air resistance, the shape and mass of the object, and the conditions of the surface on which the object lands.

5. How accurate is this calculation?

This calculation can provide a fairly accurate estimate of the impact speed of a dropped object. However, it is important to keep in mind that it does not take into account all factors that may affect the impact speed, so the actual speed may differ slightly from the calculated value.

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