Aim: How do projectiles differ when launched at an angle? Angled Projectiles Aim: How do projectiles differ when launched at an angle?

Vector Components Ax = A cos θ Ay = A sin θ Two dimensional motion is where an object travels in the horizontal and vertical axes at the same time However in order to simplify 2D problems you typically break the vector(s) into its x and y COMPONENTS (parts) This is done using Trigonometry; and in most cases (not all)… Ax = A cos θ Ay = A sin θ Horizontal Component Vertical Component Any Vector

Determine the horizontal and vertical components of the above vector Example 50m/s 35° Determine the horizontal and vertical components of the above vector

2D Motion Problems When dealing with 2D motion, always keep these important points in mind When necessary, calculate the COMPONENTS of the 2D vector A 2D vector usually has a MAGNITUDE and an ANGLE NEVER use the 2D vector in ANY calculations besides determining the components The values in the two axes are INDEPENDENT OF EACH OTHER Horizontal values only affect horizontal values while vertical values only affect vertical values NEVER MIX THE AXES! However, TIME is the only value that can be used in BOTH AXES

Angled Projectiles Angled projectiles combine INITIAL VERTICAL UPWARD MOTION and CONSTANT HORIZONTAL MOTION All projectiles follow a PARABOLIC PATH Launching the projectile at 45° will give the LONGEST RANGE (horizontal distance) Launching the projectile at 90° will give the HIGHEST HEIGHT and LONGEST AIR TIME Complimentary angles result in the same range but different times

Angled Projectile Rules vy = 0m/s tup = tdown θ ttotal = 2×tup vix = vi cosθ ax = 0m/s2 Horizontal Velocity is Constant viy = vi sinθ ay = g = -9.81m/s2 The projectile STOPS at maximum height The final vertical velocity is equal to the initial vertical velocity but in opposite direction

Example #1 A football quarterback needs to throw a 40m touchdown pass with 3 seconds left in the 4th quarter. Assuming he throws the ball at a 45° angle, how fast must he throw the ball?

Example #2 If Lionel Messi can kick a ball at a speed of 28.9m/s at an angle of 30°, (a) how high and (b) how long will it take the ball to reach maximum height? (a) (b)

Example #3 The M19 mortar has a muzzle velocity of 168m/s. If a shell were to be fired at an angle of 50°, (a) how high will the shell reach and (b) how far will it land? (a)

Example #3 The M19 mortar has a muzzle velocity of 168m/s. If a shell were to be fired at an angle of 50°, (a) how high will the shell reach and (b) how far will it land? (b)

SUMMARY How do you calculate the components of 2D vector? Describe the path an angled projectile takes What angles provide the… Longest range? Longest hang time? List the horizontal and vertical rules for angled projectiles What is the vertical velocity and acceleration at the pinnacle of an angled projectile?