Module 26  Vectors  
Introduction  Lesson 1  Lesson 2  Lesson 3  SelfTest  
Lesson 26.3: Projectile Motion  
It is often useful to find a vector function that models the path of a projectile. Such a function can yield the particle's position at time t as well as its velocity and acceleration. This lesson will explore finding the function that models the path of such an object given some initial information. Finding the Position Vector A projectile is fired from ground level. If the starting point for the projectile is considered to be the origin and if air resistance is neglected, the position vector for the projectile at time t is where v_{0} is the initial velocity of the projectile, is the angle from the horizontal at which the projectile is fired and g is the acceleration due to gravity. When t is measured in seconds and distance is measured in feet, the acceleration due to gravity is given by g = 32 ft/sec each second. If distance is measured in meters, g = 9.8 m/sec^{2}. The position vector can also be represented with the corresponding parametric equations A Specific Example Suppose a projectile is fired at an angle of = 20° from the horizontal with an initial velocity of 180 ft/sec. Graph the path of the projectile using 32 ft/sec^{2} for g.
26.3.1 Use the trace key to approximate when the projectile reaches its highest point and estimate the position vector at the highest point. Click here for the answer. Recalling Previous Functions If you have not cleared the variables X_{2T}, Y_{2T} and X_{3T}, Y_{3T} since Lesson 26.2, these variables should still be defined as the velocity and acceleration vectors for the position vector stored in X_{1T} and Y_{1T}. If you have cleared these variables, redefine them as they were defined in Lesson 26.2.
26.3.2 Select the velocity parametric equations. Evaluate the velocity vector at the value of t when the projectile reaches its highest point. Interpret the meaning of this vector in terms of the projectile motion. Click here for the answer.
26.3.3 Select the acceleration parametric equations. Evaluate the acceleration vector at several values of t. Interpret the meaning of this vector in terms of the projectile motion. Click here for the answer. 

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