Physics Lesson 11/9

Physics Lesson 11/9

Angled Projectile Motion

Open Ended

Journal: What will be the trajectory of a projectile launched at an angle?

Angled Launches

• When a projectile is launched at an angle, the initial velocity has a vertical component as well as a horizontal component.

• If the object is launched upward, like a ball tossed straight in the air, it rises with a slowing speed, reaches the top of its path where its speed is instantaneously zero, and descends with increasing speed.

• The upper diagram shows the separate vertical and horizontal motion motion diagrams for the trajectory.

• Note the symmetry of the vertical

• At each point in the vertical direction, the velocity of the object has the same velocity going upward as it does downward.

• The only difference is the direction of the two velocities are opposite.

• When solving problems it is sometimes useful to consider symmetry to determine unknown quantities.

• The lower diagram defines two quantities associated with the trajectory.

• One is the maximum height, which is the height of the projectile when the vertical velocity is 0 and the projectile only has its horizontal velocity component.

• The other quantity is the range (R), which is the horizontal distance the projectile travels when the initial and final heights are the same.

• Not shown is the flight time or hang time.

Forces from Air

Notice how air affects the trajectory of a projectile.

Open Ended

Example Problem - A ball is launched at 4.5 m/s a6 66 degrees above the horizontal. It starts and lands at the same distance from the ground. What are the maximum height above its launch level and the flight time of the ball?

Open Ended

Exit Ticket: If a ball is tossed into the air with a maximum velocity of 11.0 m/s, what will be its maximum height?