HELP A question on Kinematics in 2D & 3D?

In summary, the question is about a gun placed on a hill with a given angle and muzzle velocity. The solution involves separating the problem into two 1D equations for the x and y axes. The coordinates for the point of impact can be used to find the flight time and ultimately the distance at which the bullet will fall.
  • #1
Kudo Shinichi
109
1
HELP! A question on Kinematics in 2D & 3D?

Homework Statement



A gun is placed at the base of a hill whose slope makes an angle alpha with the horizontal. If the gun is set at an angle theta with the horizontal and has a muzzle velocity Vo, find the distance, measured along the hill, at which the bullet will fall.


The Attempt at a Solution


I know that I need to separate this question into two equations/ two 1D problems (x-axis and y axis)
Velocity for x = Vo* cos(Θ-α) - g * t * sin(α)
X = Xo + Vo * t * cos(Θ-α) - 0.5 * g * t^2 * sin(α)
Velocity for y = Vo* sin(Θ-α) - g * t * cos(α)
Y = Yo + Vo * t * sin(Θ-α) - 0.5 * g * t^2 * cos(α)

But how can i figure out Vo, Θ, α, Xo, t and Yo

Please help me.
 
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  • #2


Seems you've set your axes up so that the x-axis runs along the slope. What condition occurs at the point of impact that you can use. That is, what will the value of the y-axis be?
 
  • #3


Kurdt said:
Seems you've set your axes up so that the x-axis runs along the slope. What condition occurs at the point of impact that you can use. That is, what will the value of the y-axis be?

Do you mean set subsitute one of the variable in y equation from x equation?
 
  • #4


Yes. What will the y position be with the coordinates you chose when the ball lands? You can then get an expression for the flight time and sub it into the x equation which will give you the distance when t is the total flight time.
 

1. What is Kinematics in 2D and 3D?

Kinematics in 2D and 3D is a branch of physics that studies the motion of objects in two and three dimensions, respectively. It involves analyzing the position, velocity, and acceleration of objects without considering the forces that cause the motion.

2. What is the difference between 2D and 3D kinematics?

The main difference between 2D and 3D kinematics is the number of dimensions being considered. In 2D kinematics, motion is analyzed in two dimensions, usually represented by the x and y axes. In 3D kinematics, motion is analyzed in three dimensions, typically represented by the x, y, and z axes.

3. How is kinematics used in real life?

Kinematics is used in real life in various fields, including engineering, robotics, and sports. It helps in designing and optimizing machines and structures, predicting the trajectory of projectiles, and analyzing the movements of athletes.

4. What are some key concepts in kinematics?

Some key concepts in kinematics include displacement, velocity, acceleration, and time. Displacement is the change in position of an object, velocity is the rate of change of displacement, and acceleration is the rate of change of velocity. Time is also a crucial concept as it is used to measure the duration of motion.

5. How is kinematics related to other branches of physics?

Kinematics is closely related to other branches of physics, such as dynamics and mechanics. Dynamics deals with the forces that cause motion, while kinematics focuses on the motion itself. Mechanics combines both kinematics and dynamics to study the motion of objects in relation to the forces acting upon them.

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