Projectile Motion Falling Objects Ms Donis So far

Projectile Motion + Falling Objects Ms. Donis

So far, we have 2 kinematic equations:

Projectile Motion ● Free-flying objects are also called projectiles ○ These are objects that are thrown or dropped in the presence of Earth’s gravity to experience a constant acceleration directed toward the center of the Earth. ● Assumptions: ○ Free- fall acceleration is the same for all objects, regardless of the mass ○ The value for free-fall acceleration on Earth’s surface is ag= -9. 8 m/s 2 ○ Air resistance is negligible

Let’s say you’re throwing a rock up in the air… The initial velocity is 19. 6 m/s You want to find the displacement of the rock.

Let’s say you’re throwing a rock up in the air. . . ● You want to study the rock’s movement over 4 seconds in time. ● You develop three different graphs: ○ Displacement vs. time ○ Velocity vs. time ○ Acceleration vs. time

Example 1: A ball is thrown vertically upward: a) b) c) d) e) What happens to the ball’s velocity while the ball is in the air? What is its velocity when it reaches maximum altitude? What is its acceleration when it reaches maximum altitude? What is the acceleration just before it hits the ground? Does its acceleartion increase, decrease or remain constant?

Example 2: Finding Final Velocity (Equation #1)

Example 3 : Finding Final velocity (Equation #1) A diver jumps from a diving board into a swimming pool. What is the diver’s velocity right before he hits the water. It takes him 5 seconds before he goes underwater.

Example 4 : Finding displacement (Equation #2) A squirrel drops an acorn on the head of an unsuspecting dog. The acorn falls for 0. 90 seconds before it hits the dog’s head. Find its displacement

Example 5: Finding displacement (Equation #2) A softball thrown straight up at 17. 5 m/s is caught 3. 60 seconds later. How high does the ball rise?

Example 6 : Finding Final velocity + Displacement A small fish is dropped by a pelican that is rising steadily at 0. 50 m/s. After 2. 5 s, what is the velocity of the fish? What is the displacement of the pelican? What is the displacement of the fish? How far below is the fish from the pelican?

Example 7: Finding time A falcon dives at a pigeon. The falcon starts from rest with free-fall acceleration. If the pigeon is 76 m below, how long does it take for the falcon to reach the pigeon?

One more equation: Finding Final Velocity

Example 8: Finding final velocity (Equation #3) A worker drops a wrench from the top of a tower 80 meters tall. What is the velocity of the wrench when it strikes the ground?

Example 9: Finding final velocity (Equation #3) A surface probe on the planet Mercury falls 17. 6 m downward from the ledge. If free-fall acceleration near Mercury is -3. 70 m/s 2, what is the probe’s velocity when it reaches the ground?