# Cannon Hits Cliff: Calculating Minimum Muzzle Velocity & Distance Past Edge

• Yahaira.Reyes
In summary, the cannon needs a minimum muzzle velocity of V0 to clear the top of the cliff, which can be calculated using the equations x=x0 + V0t, Vy= v0y-gt, y=y0+v0yt-1/2gt^2, and vf^2=vi^2-2ax, where the mass of the shell is not relevant. The x-component of the initial velocity is VO cos(43) and the y-component is VO sin(43). Time can be calculated in terms of x and then substituted into the equation for y. Knowing that x=60 and y=25, the necessary velocity V0 can be determined.
Yahaira.Reyes
A connon, located 60 m from the base of a vertical 25.0m tall clift, shoots a 15 kg shell at 43.0 degrees above the horizontal toward the cliff.

A) what must the minimum muzzle velocity be for the shell to clear the top of the cliff?
B) The ground at the top of the cliff is level, with a constant elevation of 25.0 m above the cannon. Under the conditions of part (A), how far does the shell past the edge of the cliff?

x=x0 + V0t
Vy= v0y-gt
y=y0+v0yt-1/2gt^2
vf^2=vi^2-2ax

I am a little throw off by the kg of the shell. I do not know how to start the prob.

As is always the case with "gravity" problems, the mass of the shell is irrelevant. Ignore it. Use precisely the equations you have with one addition: If V0 is the initial muzzle velocity, then the x-component is VO cos(43) and the y-component is VO sin(43).

wouldn't I need to calculate the time ? All of the equations require time.

Yahaira.Reyes said:
wouldn't I need to calculate the time ? All of the equations require time.

no, you can put time in function of x, and then substitute in equation of y, getting y in funtion of x.

that gives the y coordinate in respect with x. with x=60 and y=25,you know that there will be a velocity V0 needed.(this after you've done the cos/sin thing HallsofIvy told and well.)

## 1. How do you calculate the minimum muzzle velocity?

The minimum muzzle velocity can be calculated using the formula: Vmin = √(2gh), where Vmin is the minimum muzzle velocity, g is the acceleration due to gravity, and h is the height of the cliff.

## 2. What is the importance of calculating the minimum muzzle velocity?

Calculating the minimum muzzle velocity is important because it helps determine the minimum amount of force required to launch a cannonball over a cliff. This information is crucial for ensuring the safety and accuracy of the cannon, as well as for predicting the distance the cannonball will travel.

## 3. Can the minimum muzzle velocity be calculated for any height of cliff?

Yes, the formula for calculating the minimum muzzle velocity can be used for any height of cliff. However, it is important to note that the accuracy of the calculation may be affected by other factors such as air resistance and the angle of the cannon.

## 4. How can the distance past the edge of the cliff be calculated?

The distance past the edge of the cliff can be calculated using the formula: d = V02/g, where d is the distance past the edge of the cliff, V0 is the initial velocity of the cannonball, and g is the acceleration due to gravity. This formula assumes that the cannonball is launched at an angle of 45 degrees.

## 5. How does air resistance affect the calculations?

Air resistance can affect the calculations by slowing down the velocity of the cannonball and reducing its distance traveled. However, for shorter distances and lower velocities, the effect of air resistance is minimal and can be ignored. For more accurate calculations, the air resistance can be taken into account using more complex equations.

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