Projectile Motion!!!

Objectives For My Page:
 

• Students will be able to gain extensive knowledge on projectile motion

• Students will learn how to use the kinematic equations to solve projectile motion equations

• Here is a story for you:

               Pat and Pete were playing a game of catch. Pat throws the ball at pete at 36 m/s at a 26.76 degree angle. assuming that the ball originally has no height and that pete is .123 yards away, how close does the ball come to pete?

         Using the projectile motion equations you can find out the answer to this problem (look at my website to find the equations.)
 

• Barry Bostwick and Halle Berry are drinking Pepsi Twist. Halle Berry says she has never heard of Barry Bostwick to whick Barry replies by throwing his Pepsi Twist at Halle. Barry throws the can at 6 m/s at a 35 degree angle and Halle is standing 10 meters away. Does it hit Halle?

           Once again you can use the kinematic equations (from this site) to solve the problem.

Concepts for Projectile Motion:
 

• If the projectile is launched at a 0 degree angle it will not travel upwards into the air at all.

• If the projectile is launched at a 45 degree angle it will go the farthest horizontal distance.

• If the projectile is launched at a 90 degree angle it will go the farthest vertical distance.

• If the projectile's time in the air is more than double the time received from the first kinematic, then it is hitting an object below the original launching position.

• If the projectile's time in the air is less than double the time received from the first kinematic, then it is hitting an object above the original launching position.

Formulas and Explanations:
 

• Kinematic Equations:

                1.  V = Vo  +  at
                2.  X = 1/2 ( Vo + V ) t
                3.  X = Vot + 1/2at^2
                4.  V^2 = Vo^2 + 2ax

                            Key

                Vo=Original Velocity (meters/sec)
                V=Final Velocity (meters/sec)
                X=Distance (meters)
                T=Time (sec.)
 

How to solve a Projectile Motion Problem:
 

• Solve for X and Y using:
• X = Vo Cosine Angle
• Y = Vo Sine Angle

• Use the 1st kinematic equation to solve for time
• Multiply the time by 2

• Plug the time and the value for X (which goes into Vh) back into the formula X=Vht to find the horizontal distance

• Plug the time and the Value for Y (which goes into Vv) back into the formula X=Vv(1/2t) to solve for vertical distance.

1.   A rocket is fired at a 40 degree angle at 80m/s solve for it's time in the air.

                                    X=80m/s Cos 40
                                    X=61.28 m/s

                                    Y=80m/s Sin 40
                                    Y=51.42 m/s

                                       V= Vo + at
                            0m/s = 80m/s + (-9.8m/S^2)t
                                    t = 8.16 sec x 2
                                  t = 16.32 sec

2.  I throw a cheese sandwich at pat at a 20 degree angle at 453m/s how far (horizontally) does it travel?

                                 X = 453m/s Cos 20
                                    X = 425.68 m/s

                                 Y = 453m/s Sin 20
                                    Y = 154.94 m/s

                                       V = Vo + at
                            0m/s = 453m/s + (-9.8m/s^2)t
                             t = 46.22 sec x 2 = 92.44 sec

                                        Xh = Vh x t
                             Xh = (425.68m/s) x 92.44 sec
                                 Xh = 39349.86 m

3. A pitcher of applesauce is kicked at a 55 degree angle at 45 m/s solve for its time in the air.

                                    X = 45m/s Cos 55
                                       X = 25.81 m/s

                                    Y = 45m/s Sin 55
                                        Y = 36.86 m/s

                                        V = Vo + at
                               0m/s = 45m/s + (-9.8m/s)t
                               t = 4.59 sec x 2 = 9.18 sec