IesusDev

Use the WASD keys to rotate the ship and the arrow keys to move it.

Initial Confuguration

Current information

tt: 0.00 ss
Sphere position: xx: 0.00, Y: 0.00, Z: 0.00
Ship position: X: 0.00, Y: 0.00, Z: 0.00
Kinetic enegery: 200.00 J
Potential energy: 0.00 J
Total energy: 200.00 J

Absolute Information

Max height: 10.19
Highest Position X: 20.39, Y: 0.00, Z: 10.19
Maximum height time: 1.44
Final position: 40.77, 0.00, 0
Final position time: 2.88
Initial kinectic energy: 200 J
Initial potential energy: 0.00 J

Calculator

0 ss

2.88ss

Information at time tt

tt = 0.00 s
xx = 0.00, yy = 0.00, zz = 0.00
vxv_x = 14.14, vyv_y = 14.14, vzv_z = 0.00
vv = 20.00
EkE_k = 200.00 J
EpE_p = 0.00 J
EtE_t = 200.00 J

Fórmulas

Initial velocity

v0x=v0⋅cos⁡(φ)⋅cos⁡(θ)v_{0x} = v_{0} \cdot \cos(\varphi) \cdot \cos(\theta)
v0y=v0⋅sin⁡(φ)v_{0y} = v_{0} \cdot \sin(\varphi)
v0z=v0⋅cos⁡(φ)⋅sin⁡(θ)v_{0z} = v_{0} \cdot \cos(\varphi) \cdot \sin(\theta)

Position

x(t)=x0+v0x⋅tx(t) = x_0 + v_{0x} \cdot t
y(t)=y0+v0y⋅t−12gt2y(t) = y_0 + v_{0y} \cdot t - \frac{1}{2} g t^2
z(t)=z0+v0z⋅tz(t) = z_0 + v_{0z} \cdot t

Velocity as a time function

vx(t)=v0xv_{x}(t) = v_{0x}
vy(t)=v0y−g⋅tv_{y}(t) = v_{0y} - g \cdot t
vz(t)=v0zv_{z}(t) = v_{0z}

Energy

Ek=12mv2E_k = \frac{1}{2} m v^2
Ep=mgyE_p = m g y
Et=Ek+EpE_t = E_k + E_p

Maximum height

ymax=y0+v0y22gy_{max} = y_0 + \frac{v_{0y}^2}{2g}
tmax=v0ygt_{max} = \frac{v_{0y}}{g}
xmax=x0+v0x⋅tmaxx_{max} = x_0 + v_{0x} \cdot t_{max}
zmax=z0+v0z⋅tmaxz_{max} = z_0 + v_{0z} \cdot t_{max}

Velocities at maximum height

vx(tmax)=v0xv_{x}(t_{max}) = v_{0x}
vy(tmax)=0v_{y}(t_{max}) = 0
vz(tmax)=v0zv_{z}(t_{max}) = v_{0z}
v(tmax)=v0x2+v0z2v(t_{max}) = \sqrt{v_{0x}^2 + v_{0z}^2}

Final position

xfinal=x0+v0x⋅tfloorx_{final} = x_0 + v_{0x} \cdot t_{floor}
yfinal=0y_{final} = 0
zfinal=z0+v0z⋅tfloorz_{final} = z_0 + v_{0z} \cdot t_{floor}
tfloor=v0y+v0y2+2gy0gt_{floor} = \frac{v_{0y} + \sqrt{v_{0y}^2 + 2gy_0}}{g}

Velocities at final position

vx(tfloor)=v0xv_{x}(t_{floor}) = v_{0x}
vy(tfloor)=v0y−g⋅tfloorv_{y}(t_{floor}) = v_{0y} - g \cdot t_{floor}
vz(tfloor)=v0zv_{z}(t_{floor}) = v_{0z}