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What is motion in multiple dimensions?
Motion in multiple dimensions is the description of an object’s motion in 3D space, taking into account its coordinates along the x, y, and z axes.
What is the first thing to do when describing motion in multiple dimensions?
The first thing to do when describing motion in multiple dimensions is to set up a coordinate system with 3 axes, usually x, y, and z.
How is average velocity defined in motion in multiple dimensions?
Average velocity is defined in motion in multiple dimensions as the change in coordinates (x, y, z) over time (t) or (Δx/Δt, Δy/Δt, Δz/Δt).
How is instantaneous velocity defined in motion in multiple dimensions?
Instantaneous velocity in motion in multiple dimensions is the limit of the average velocity as the time interval becomes smaller and smaller, or (dx/dt, dy/dt, dz/dt).
How is speed found in motion in multiple dimensions?
Speed is found in motion in multiple dimensions using the Pythagorean Theorem, where speed (v) = √(vx^2 + vy^2 + vz^2).
How is average acceleration defined in motion in multiple dimensions?
Average acceleration in motion in multiple dimensions is the change in velocity (vx, vy, vz) over time (t) or (Δvx/Δt, Δvy/Δt, Δvz/Δt).
How is instantaneous acceleration defined in motion in multiple dimensions?
Instantaneous acceleration in motion in multiple dimensions is the limit of the average acceleration as the time interval becomes smaller and smaller, or (d^2x/dt^2, d^2y/dt^2, d^2z/dt^2).
Are the motions of an object along each coordinate independent in motion in multiple dimensions?
Yes, the motions of an object along each coordinate are independent in motion in multiple dimensions.
Do Newton’s Laws apply to each coordinate separately in motion in multiple dimensions?
Yes, Newton’s Laws apply to each coordinate separately in motion in multiple dimensions.
What is projectile motion?
Projectile motion is the motion of an object in two or more dimensions under the influence of gravity.
What is the force on an object in projectile motion?
In projectile motion, the force on an object is -mg due to gravity, where m is the mass of the object and g is the acceleration due to gravity.
Is there any force in the x direction in projectile motion?
No, there is no force in the x direction in projectile motion.
What is the acceleration in the x direction in projectile motion?
The acceleration in the x direction in projectile motion is zero.
What is the acceleration in the y direction in projectile motion?
The acceleration in the y direction in projectile motion is -g due to gravity.
How is motion in projectile motion broken up?
Motion in projectile motion is broken up into the motion in the x direction (horizontal) and the motion in the y direction (vertical).
What happens to an object in projectile motion when it reaches the edge of a surface?
When an object in projectile motion reaches the edge of a surface, it has a non-zero x velocity but zero y velocity. Since there is no x acceleration, the object keeps the same x velocity. The object has acceleration in the y direction due to gravity, so it starts to fall and pick up y velocity at a rate of 10 m/s^2.
What happens to an object in projectile motion when it is thrown at some angle?
When an object is thrown at some angle, it experiences a combination of vertical and horizontal motion, resulting in a curved path known as projectile motion. The vertical component of the motion is affected by gravity, causing the object to accelerate downward, while the horizontal component remains constant unless acted upon by a force.
What is the acceleration due to gravity?
The acceleration due to gravity is -g, which is 10 m/s^2 directed downwards.
What is the equation for the speed of an object in projectile motion?
The equation for the speed of an object in projectile motion is v = sqrt(vx^2 + vy^2), where vx is the velocity in the x direction and vy is the velocity in the y direction.
Range
The distance a projectile travels horizontally is called its range. R
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