Need help with a confounding projectile motion problem.

In summary, the problem is to find the initial velocity of a cannonball fired at a 45 degree angle that lands 100 meters away. The person has attempted to use kinematic equations but has trouble solving for two variables with only one equation. They are asking for help and it is suggested to use two separate equations for horizontal and vertical displacement. The formula for horizontal range is provided and it is mentioned that air resistance may play a role in the calculation. After receiving help from others, the person believes they have found the answer.
  • #1
MisterNi
4
0
Ok, here's the problem:

A cannon angled at 45 degrees above the horizontal is fired. The cannonball lands 100 meters away. What is the initial velocity?

I've tried using the kinematic equations, but I always end up with at least 2 variables with 1 equation. I'm just completely stumped. Any help to nudge me in the right direction would be greatly appreciated. Thank you.
 
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  • #2
Post your calculations so that we can show you the solution/errors.
 
  • #3
You have two equations: one to solve for the horizontal displacement and one to solve for the vertical displacement.
 
  • #4
You certainly should have two equations- one for the horizontal position and one for the vertical position. Your two variables will be the horizontal component of initial velocity (which is equal to the vertical component because the angle is 45 degrees) and time.
 
  • #5
May use the formula for horizontal range of a projectile

R = u^2sin(2theeta)/g
 
  • #6
I'd say that your army is in trouble if you can only shoot 100 metres.
Actually, I just wanted to clarify if this is neglecting air resistance. That makes a big difference.
 
  • #7
Thanks for BobG, HallsofIvy and mukundpa, I think I got the answer.
 

1. How do I determine the initial velocity of a projectile?

The initial velocity of a projectile can be determined by using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In most projectile motion problems, the initial velocity is given or can be calculated using other known values such as the angle of launch and the range of the projectile.

2. What is the difference between horizontal and vertical components of projectile motion?

The horizontal component of projectile motion refers to the motion of the projectile along the x-axis, while the vertical component refers to the motion along the y-axis. The horizontal component is affected by the initial velocity and remains constant throughout the motion, while the vertical component is affected by gravity and changes over time.

3. How do I find the maximum height of a projectile?

The maximum height of a projectile can be found by using the equation h = (u^2 sin^2θ)/(2g), where h is the maximum height, u is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity. This equation assumes that the projectile is launched from a horizontal surface and lands on the same surface.

4. What is the range of a projectile?

The range of a projectile is the horizontal distance it travels before hitting the ground. It can be calculated using the equation R = (u^2 sin2θ)/g, where R is the range, u is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity. This equation also assumes that the projectile is launched from and lands on a horizontal surface.

5. How does air resistance affect projectile motion?

Air resistance can affect projectile motion by reducing the speed and altering the trajectory of the projectile. This is due to the force of air resistance acting in the opposite direction of the projectile's motion. In most cases, air resistance can be ignored in projectile motion problems unless specifically stated otherwise.

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