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6 days ago · In the case where the initial height is 0, the formula can be written as: V y 0 t − g t 2 / 2 = 0. V_\mathrm {y0} t - g t^2 / 2 = 0 V y0. . t−gt2/2 = 0. Then, from that equation, we find that the time of flight is. \qquad t = 2 \frac {V_\mathrm {y0}} {g} = 2 \frac {V_0} {g} \sin\alpha t = 2 gV y0 = 2 gV 0 sin α.
A simple "jiggle" recipe. So, we would like to make a 3D point \( p_n \in \mathbb R^3\) at the \( n^{\text th} \) animation frame jiggle. One way to do this is to have a target point (\(target \in \mathbb R^3\)) which will attract \( p_n \) in such a way that it "jiggles" around his \( target \).
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- Variables
- Relevant Formulae, Condensed Version
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I'm using the subscript yy to denote stuff in the perpendicular direction (along the yy or hh axis), and xx for stuff in the parallel direction (along xx). I'll use uu for initial velocities and vvfor final velocities. The initial and final refer to "just before/after a bounce", and "just before/after an arc", where "bounce" refers to the moment wh...
For a bounce
vy=−euyvy=−euyvx=ux+μ(e−1)uyvx=ux+μ(e−1)uy These vvs become uus for the upcoming arc. Bounces are pretty much instantaneous. If you want to consider the time factor, you need to know the shape and young's modulus of the object.
For an arc
The arc will be executed in a time tarc=2uy/gtarc=2uy/g, and will attain a maximum height ymax=u22gymax=u22g During this time:(tt is the time since the arc started, NOT the total time)y=uy−12gt2y=uy−12gt2x=uxtx=uxt At the moment the arc finishes, vx=uxvx=uxvy=−uyvy=−uyThese vvs become the uus for the next "bounce"
SUVAT equations
See suvat-equations. In this case, ay=−g,ax=0ay=−g,ax=0, and ss is distance travelled in relevant direction. You can apply these equation separately for xx and yy.
Bouncing
Here, NN is normal force. ff is the friction force. JJ refers to impulse, pp to momentum.Frictionf=±μNdirection can varyf=±μNdirection can varyImpulseJy=∫NdtJy=∫NdtJx=∫fdtJx=∫fdtWe can combine these to get Jx=±μJyJx=±μJyWe take the sign −− in this case, as friction opposes motion, and the motion in xxdirection is positive. J=Δp=m(v−u)for both axesJ=Δp=m(v−u)for both axes Combining all these, you can get the bounciness equations. Note: if you want your ball to have a spin as well, the equation...
The electrical power calculator helps you compute the power consumed by electrical devices. The electric field calculator finds the magnitude of the electric field generated by a point charge. The electric motor torque calculator provides the relation between rotational speed, power, and torque in the shaft.
Apr 18, 2024 · Use this trajectory calculator to find the flight path of a projectile. Type in three values: velocity, angle, and initial height, and in no time, you'll find the trajectory formula and its shape. Keep reading if you want to check the trajectory definition as well as a simple example of calculations.
Projectile motion is the motion of an object thrown (projected) into the air when, after the initial force that launches the object, air resistance is negligible and the only other force that object experiences is the force of gravity. The object is called a projectile, and its path is called its trajectory.
Feb 20, 2022 · As in many physics problems, there is more than one way to solve for the time to the highest point. In this case, the easiest method is to use \(\displaystyle y=y_0+\frac{1}{2}(v_{0y}+v_y)t\). Because y0 is zero, this equation reduces to simply \(\displaystyle y=\frac{1}{2}(v_{0y}+v_y)t\).
