The total time of flight of the football is 3.61 seconds. If both sides of the equation are divided by -9.8 m/s/s, the equation becomes 3.61 s = t By subtracting 17.7 m/s from each side of the equation, the equation becomes -35.4 m/s = (-9.8 m/s/s) The physics problem now takes the form of an algebra problem. By substitution of known values, the equation takes the form of -17.7 m/s = 17.7 m/s + (-9.8 m/s/s) An organized listing of known quantities in two columns of a table provides clues for the selection of a useful strategy.įrom the vertical information in the table above and the second equation listed among the vertical kinematic equations (v fy = v iy + a y*t), it becomes obvious that the time of flight of the projectile can be determined. There are a variety of possible strategies for solving the problem. The solution of the problem now requires the selection of an appropriate strategy for using the kinematic equations and the known information to solve for the unknown quantities. The unknown quantities are the horizontal displacement, the time of flight, and the height of the football at its peak. This is due to the symmetrical nature of a projectile's trajectory. The table also indicates that the final y-velocity (v fy) has the same magnitude and the opposite direction as the initial y-velocity (v iy). This is due to the fact that the horizontal velocity of a projectile is constant there is no horizontal acceleration. In this case, the following information is either explicitly given or implied in the problem statement:Īs indicated in the table, the final x-velocity (v fx) is the same as the initial x-velocity (v ix). The solution continues by declaring the values of the known information in terms of the symbols of the kinematic equations - x, y, v ix, v iy, a x, a y, and t. In this case, it happens that the v ix and the v iy values are the same as will always be the case when the angle is 45-degrees. The solution of any non-horizontally launched projectile problem (in which v i and Theta are given) should begin by first resolving the initial velocity into horizontal and vertical components using the trigonometric functions discussed above. Determine the time of flight, the horizontal displacement, and the peak height of the football. To illustrate the usefulness of the above equations in making predictions about the motion of a projectile, consider their use in the solution of the following problem.Ī football is kicked with an initial velocity of 25 m/s at an angle of 45-degrees with the horizontal. The topic of components of the velocity vector was discussed earlier in Lesson 2.
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