speed horizontal component at t=0
|
v0x=v0cos(θ) |
speed vertical component at t=0
|
v0y=v0sin(θ) |
acceleration horizontal component
|
ax=0 |
acceleration vertical component
|
ay=−g |
speed vertical component at any time
|
vx=v0cos(θ) |
speed vertical component at any time
|
vx=v0sin(θ)−gt |
velocity magnitude
|
v=vx2+vy2 |
horizontal displacement
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x=v0tcos(θ) |
vertical displacement
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y=v0tsin(θ)−21gt2
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displacement magnitude
|
Δr=x2+y2 |
range d for initial height y0
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d=gvcosθ(vsinθ+v2sin2θ+2gy0)
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range if y0=0
|
d=gv2sin2θ |
initial velocity
|
v0=xsin2θ−2ycos2θx2g
|
time of flight |
t=∣g∣2v0tsin(θ)
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time of flight for height y0
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t=vcosθd=gvsinθ+(vsinθ)2+2gy0
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time of flight to the target position
|
t=v0cos(θ)x |
time to reach maximum height
|
thmax=∣g∣v0sin(θ)
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maximum height |
hmax=2∣g∣v02sin2(θ)
|
maximum height for known (x,y) position and
angle (θ)
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hmax=4(xtanθ−y)(xtanθ)2
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relation between d and hmax
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hmax=4dtanθ |
maximum distance (θ=45∘C)
|
dmax=∣g∣v2 |
angle of reach for shallow trajectory
|
θ=21arcsin(v2gd)
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angle of reach for steep trajectory
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θ=21arccos(v2gd)
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angle required to hit a coordinate (x,y)
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θ=arctan(gxv2±v4−g(gx2+2yv2))
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total path length of the trajectory
|
L=gv02(sinθ+cos2θ⋅tanh−1(sinθ))
|