cite 5 examples of motion in 2 to 3 dimensions. illustrate your 5 examples to position displacement and acceleration in vector notation
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Expert's answer
2021-02-11T17:10:44-0500
The position of a particle can be described by a position vector, with respect to a reference origin.
r=xi^+yj^+zk^
The displacement of a particle is the change of the position vector during a certain time.
Δr=(x2i^+y2j^+z2k^)−(x1i^+y1j^+z1k^)
Δr=(x2−x1)i^+(y2−y1)j^+(z2−z1)k^
Following the same definition as in average velocity,
averageacceleration=timeintervalchangeinvelocity
aavg=Δtv2−v1=ΔtΔv
If we shrink Δt to zero, then the average acceleration value approaches to the instant acceleration value, which is the derivative of velocity with respect to time:
a=dtdv
a=dtd(vxi^+vyj^+vzk^) =
=(dtdvxi^+dtdvyj^+dtdvzk^)
=(axi^+ayj^+azk^)
examples of motion in 2 dimension: Circular Motion, Projectile Motion, Uniform Circular Motion
In Projectile motion:
Examples in sports: Tennis, Baseball, Football, Lacrosse, Racquetball, Soccer…
A particle moves in a vertical plane, with some initial velocity 𝒗𝟎; the only acceleration is the free-fall acceleration, 𝒈, directed vertically downward.
The trajectory of a projectile motion is a parabola unless the object has no horizontal component of motion in which case it is simply free fall.
The equation for the trajectory: y=xtanθo−2vo2cos2θogx2
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