Projectile motion - limited given data

In summary, the problem involves a projectile shot from a cannon at an angle of 40 degrees above the x-axis. The projectile passes over a net placed 6.0m away from the cannon horizontally. The goal is to find the muzzle speed of the cannon and the height of the net. Using the equations delta x = .5(Vf + Vi)t, Vf=at + Vi, delta x = .5at^2 + Vit, Vicos40 = X component Vi, and Visin40 = Y component Vi, the initial speed can be solved for using two equations of motion and setting the y-component of velocity to zero at 6m in the x direction. The height of the net can then be found using
  • #1
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Homework Statement


Basically, there is a projectile shot from a cannon. When shot, the projectile passes over a net, just barely, which is placed 6.0m away from the cannon, horizontally. The cannon is angled at 40 degrees above the x-axis.

The problem is asking for the muzzle speed of the cannon and how high the net is.

Homework Equations


delta x = .5(Vf + Vi)t
Vf=at + Vi
delta x = .5at^2 + Vit
Vicos40 = X component Vi
Visin40 = Y component Vi

The Attempt at a Solution


I know that delta x would be the 6.0m, X component acceleration is 0, and Y component acceleration is -9.8m/s^2. The problem i am running into is working with the limited number of givens here. I know i need to solve for the time it takes to travel to the net(6.0m horizontally). I'm sure it will involve several equations and substitutions to solve for algebraically(we are using non-calc methods in the course), but I'm not sure where to go with this problem.
 
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  • #2
I'd solve for muzzle speed first. you have the correct equations for the components of speed. Now you need to set up two equations of motion. The y-component should be set up for speed and the x component for distance. Now you know that at 6m in the x direction the y-component of velocity will be zero. You can rearrange these two equations to find the initial speed. Finding the height of the net from here should be simple.
 
  • #3
what you do know is that at some unknown t, just as the ball misses the net,

t=6m/Vo*cos40

and Yo=Vo*sin40-.5at^2. Also tan 40=yo/6. Is that enough to do it?
 

1. What is projectile motion?

Projectile motion is the motion of an object through the air or space under the influence of gravity. It follows a curved path known as a parabola.

2. What are the factors that affect projectile motion?

The factors that affect projectile motion include the initial velocity, angle of launch, air resistance, and the force of gravity.

3. How can I calculate the range of a projectile with limited given data?

To calculate the range of a projectile, you will need to know the initial velocity, angle of launch, and the height of the object. You can then use the formula R = (v^2 * sin(2θ)) / g, where R is the range, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

4. Can projectile motion be applied to real-life situations?

Yes, projectile motion is applicable to many real-life situations, such as throwing a ball, launching a rocket, or shooting a bullet. It is also used in sports, such as basketball and golf.

5. How does air resistance affect projectile motion?

Air resistance can affect projectile motion by slowing down the object and changing its trajectory. The larger the surface area of the object, the greater the air resistance will be. This can result in a shorter range and a lower maximum height for the projectile.

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