Equation Wizard V1.21 With Patch ((FREE))
Like the previous problem (and most other problems in physics), this problem is best approached using a diagram. The first displacement is due South and the resulting displacement (at 309 degrees) is somewhere in the fourth quadrant. (It is in the fourth quadrant because 309 degrees lies between 270 degrees or due South and 360 degrees or due East.) For communication sake, we will refer to the first displacement as A and the second displacement as B. Note that A + B = R. Since the magnitude and direction of the resultant is known, the x- and y-components can be determined using trigonometric functions. Since the angle of 309 degrees is expressed as a counterclockwise angle of rotation with due East, it can be used as the Theta in the equation.
Equation Wizard v1.21 With Patch
The solutions to all five of these projectile problems involve the use of kinematic equations and an appropriate problem-solving strategy. The kinematic equations and their use in projectile problems are listed and discussed elsewhere. The basic idea of the strategy is to identify three kinematic variables for either the horizontal motion or for the vertical motion. Once , three quantities in one direction is known, all other quantities in that direction can be found (or the time of flight can be found). Often, the time is then used with kinematic quantities for the second dimension in order to determine all other unknown quantities for that dimension.
Finding the vertical displacement at the peak (ypeak) demands using the original y equation with a time of 1.28 seconds (tup). This time corresponds to the time for one-half of the trajectory - the time at which the projectile will be at its highest or peak position. Substituting the viy, ay and t values into the equation
in which case the time is 2.4637 s. The time can now be combined with a y-equations to find the vertical displacement (i.e., height above the ground) when the football has traveled horizontally to the goal posts. Use the equation:
Note that the time of flight is known. Time is a scalar quantity and has no directional component associated with it; one cannot refer to the horizontal time or the vertical time. It is listed in both tables since it can be used with kinematic equations for both the x- and the y-direction.
(b) In part (a) of this problem, the initial horizontal velocity was determined to be 37.751 m/s. For projectiles, this horizontal velocity does not change during the flight of the projectile. Thus, the projectile strikes the balcony moving with a final horizontal velocity (vfx) of 37.751 m/s. If the final vertical velocity (vfy) can be determined, then it can be used with the vfx value to determine the final velocity (vf). Several kinematic equations are useable for finding the final vertical velocity (vfy). The following equation will be used:
Now we have generated two equations with two unknowns and a solution can be found for the initial velocity of the arrow. Equation 1 is used to generate an expression for t in terms of vi. This expression is then substituted into equation 2 in order to solve for the initial velocity (vi). The work is shown below.
(b) Once the car reaches the edge of the cliff and rolls off, it becomes a projectile with a vertical acceleration of 0 m/s2. The second task involves determining the time of flight of the projectile from the cliff's edge to the water below. Like all non-horizontally launched projectiles, the starting point is to determine the initial horizontal velocity (vix) and the initial vertical velocity (viy). The initial velocity (22.7 m/s) and angle (-29.0 degrees) can be resolved into initial velocity components using the equations:
SRH-W v1.1 is used for hydraulic flow simulation in rivers and runoff from watersheds, but without the sediment capability. It solves the 2D dynamic wave equations (the standard depth-averaged St. Venant equations) that are mainly used for river simulation. In addition, the diffusive wave solver is used for watershed runoff simulation and river simulation.
Version 2 solves the 2D dynamic wave equations, i.e., the depth-averaged St. Venant equations. Its modeling capability is comparable to some existing 2D models but SRH-2D claims a few boasting features. First, SRH-2D uses a flexible mesh that may contain arbitrarily shaped cells. In practice, the hybrid mesh of quadrilateral and triangular cells is recommended though purely quadrilateral or triangular elements may be used. A hybrid mesh may achieve the best compromise between solution accuracy and computing demand. Second, SRH-2D adopts very robust and stable numerical schemes with a seamless wetting-drying algorithm. The resultant outcome is that few tuning parameters are needed to obtain the final solution. SRH-2D was evolved from SRH-W which had the additional capability of watershed runoff modeling. Many features are improved from SRH-W.
While the equation editor creates complex functions usually there are one or two variables within the equation that you wish the end user to have easy access to. This is accomplished by creating a configurable user interface.
Each wizard screen will allow you to set the parameters for each of the components within the USC701. The following screen will configure channel 1 in the USC as a type J thermocouple input. Please note that no hardware changes are required to change input type or range.
The USC701 can use up to four look up tables at any one time.These table are available for use either directly when using the wizard on input components or within the equation editor. Each table has 101 points spread evenly over the required range entered by the user.
Although the new module wizard can program the USC701 to become thousands of different signal conditioning modules, USC applications have been developed as a means of extending the functionality of the USC701. The available applications can be used as they are or as a training tool to develop your own programs using the equation editor.