CHAPTER 6 SECTION 1 Projectile Motion

Objects launched either horizontally or at an angle are considered to be projectiles. All motion can be analyzed using concepts of motion and kinematics already developed. The trick, however, is that projectiles are traveling on both the x- and y- axis. Therefore, we must analyze both the horizontal and vertical motion.

Horizontal Projectiles Which would hit the ground first, an object shot horizontally out of a cannon or an object dropped from the same height? Click on the cannon to find out! Gravity will accelerate all object on Earth at a rate of 9.8m/s 2. This acceleration will take place in the vertical direction. What will change the speed of a projectile in the horizontal direction?

Horizontal Component Vertical Component No acceleration Velocity is constant Acceleration is 9.8 m/s 2 Initial velocity = 0m/s Velocity will increase as the object falls Kinematics equations will be used to solve for this component of motion Horizontal Projectiles TIME is the “tying factor.” Once you solve for time, you can apply it to both horizontal and vertical components of motion.

Final Velocity The final velocity of any projectile will the vector sum of both the horizontal and vertical velocity. To solve…  Find final horizontal and vertical velocity.  Add using Pythagorean Theorem.  Calculate the angle of impact.

Let’s Solve A Dukes of Hazard looking car drives off a cliff with a velocity of 25m/s. The car hits the ground 30m away from the base of the cliff. What is the height of the cliff? Determine the final velocity of the car.Dukes of Hazard looking car

Projectiles Launched at an Angle Projectiles can also be launched at an angle to the ground (horizontal.) If an object is launched from the same position (height) it is caught, a parabolic trajectory will exist. Symmetry is often the key to problem solving.

Symmetry Time to rise to peak = time to fall back to original height. Initial vertical velocity = final vertical velocity Horizontal distance covered as projectile rises to peak = horizontal distance covered as projectile falls back to original height.

Tying Factor and Peak Remember:  Time to complete entire trajectory is the same both horizontally and vertically  Time to rise = time to fall back to same vertical position At peak  Vertical velocity = 0m/s  Horizontal velocity will be constant

Launch Velocity When launched at an angle to the horizontal, the initial velocity (v i )will have both horizontal and vertical components. Use SohCahToa to break down into components. ViVi v iv vhvh

Special Cases Some projectiles are launched from cliffs, hot air balloons, etc. In these cases, the projectile will fall below original launch height and symmetry will end. Two methods for solving these problems:  Divide trajectory at peak. Solve for trip up then trip down as though solving for a horizontal launch.  Divide at end of symmetry point. Solve for range, etc. Solve for section below launch height.

Horizontal Vertical Equations Range Equation