Projectile Motion What is a projectile? Regardless of its path, a projectile will always follow these rules: 1. A horizontally launched projectile moves both horizontally and vertically and traces out a parabolic trajectory. (Trajectory: The parabolic path of a projectile.) 2. The horizontal and vertical motions of a projectile are completely independent of one another. a. In the absence of air resistance, there is no net horizontal force on the projectile; therefore the projectile travels with a constant horizontal velocity. b. In the absence of air resistance, gravity is the only vertical force on the projectile; therefore the projectile travels with a uniformly accelerated vertical motion. Every second, the vertical velocity of the projectile changes by 9.8 m/s (10 m/s)
3. Horizontal and vertical motion are completely independent of each other. Therefore, the velocity of a projectile can be separated into horizontal (v x ) and vertical components (v y ). v x = velocity in the x-direction v y = velocity in the y-direction 4. For a projectile beginning and ending at the same height, the time it takes to rise to its highest point equals the time it takes to fall from the highest point back to the original position. 5. For a projectile beginning and ending at the same height, the initial speed is equal to its final speed.
Questions: 1. A projectile is launched at an angle into the air. If air resistance is negligible, what is the acceleration of its vertical component of motion? Of its horizontal component of motion? 2. At what part of its trajectory does a projectile have minimum speed? 3. Supposing a snowmobile is equipped with a flare launcher that is capable of launching a sphere vertically (relative to the snowmobile). If the snowmobile is in motion and launches the flare and maintains a constant horizontal velocity after the launch, then where will the flare land (neglect air resistance)? a. in front of the snowmobile b. behind the snowmobile c. in the snowmobile 4. Suppose a rescue airplane drops a relief package while it is moving with a constant horizontal speed at an elevated height. Assuming that air resistance is negligible, where will the relief package land relative to the plane? 5. A hunter fires a gun at the same time a monkey drops a coconut as shown below. Where should the hunter aim to hit the coconut?
Horizontal Launched Projectiles d x = v x t d x = horizontal distance v x = horizontal velocity t = time d y = 4.9 x t 2 d y = vertical distance t = time A stone is thrown horizontally at +15 m/s from the top of a cliff that is 44-m high. a. How long does the stone take to reach the bottom of the cliff? b. How far from the base of the cliff does the stone strike the ground? c. Sketch the trajectory of the stone.
Horizontally Launched Projectile Practice 1. A ball is projected horizontally at velocity of 10 m/s from the top of a 50 m high cliff. A. How long is the ball in the air? B. How far from the base of the cliff does the ball land? C. What is the vertical velocity of the ball just before it strikes the ground? D. What is the horizontal velocity of the ball just before it strikes the ground? 2. A ball is projected horizontally at velocity of 8.0 m/s from the top of a 125 m high cliff. How long is the ball in the air? A. How long is the ball in the air? B. How far from the base of the cliff does the ball land? C. What is the vertical velocity of the ball just before it strikes the ground? D. What is the horizontal velocity of the ball just before it strikes the ground? 3. A ball is projected horizontally at velocity of 5.0 m/s from the top of a 10 m high cliff. How long is the ball in the air? A. How long is the ball in the air? B. How far from the base of the cliff does the ball land? C. What is the vertical velocity of the ball just before it strikes the ground? D. What is the horizontal velocity of the ball just before it strikes the ground? 4. You are trying to roll a ball off an 1.8 m high table to hit a target on the floor 2.0 m from the table's edge. With what speed should you roll the ball?
Projectiles Launched At An Angle Let s do one example to illustrate this concept: A ball is thrown with a velocity of 5 m/s at an angle of 60 above the horizontal. V yf =0 at top v yi = 4.36 m/s v xi Separate into x and y components. v yi 5 m/s 60 o v xi
Magic Chart Equations d t v I v F a d y = ½ (v yi + v yf ) t x x x x NO d y = v yi t + 4.9 t 2 x x x NO x V yf = v yi + 9.8 t NO x x x x V yf 2 = v yi 2 + 19.6 d x NO x x x Example: A ball is thrown with a velocity of 8 m/s at an angle of 30 above the horizontal. 1. Calculate the time it takes the ball to reach the apex? (time up ) 2. Determine the total time the ball is in the air? (time total ) 3. How high does the ball go? (maximum height) V xi = initial horizontal velocity V yi = initial vertical velocity V fy = final vertical velocity 4. How far (horizontally) does the ball go? (range)
Projectiles Launched at an Angle 1. A ball is projected at a 30 angle above the horizontal at velocity of 12.0 m/s from the ground. A. How long does it take the ball to reach its apex? B. How high does the ball go? C. What is the total time the ball is in the air? D. How far does the ball go? 2. A ball is projected at a 60 angle above the horizontal at velocity of 15 m/s. A. How long does it take the ball to reach its apex? B. How high does the ball go? C. What is the total time the ball is in the air? D. How far does the ball go?
3. A scared kangaroo once cleared a fence by jumping with a speed of 4 m/s at an angle of 45 with respect to the ground. A. How long does it take the ball to reach its apex? B. How high does the ball go? C. What is the total time the ball is in the air? D. How far does the ball go? 4. A soccer ball is kicked with a speed of 7.5 m/s at an angle of 20 with respect to the ground. A. How long does it take the ball to reach its apex? B. How high does the ball go? C. What is the total time the ball is in the air? D. How far does the ball go?
The Snowball Fight Mr. Grant (aka Mr. Sneaky) throws a snowball 25 m/s at an angle of 70 o at Mr. Menzella. A. Draw a picture depicting the scenario above. B. How long is the snowball in the air? C. How far does the snowball travel? D. Does the snowball hit Mr. Menzella who is standing 41.5 m away?