PROJECTILE MOTION

Projected vs DroppedBoth balls will hit the ground at the same time whether dropped vertically or fired horizontally, bc gravity is the force that is pulling on them equally downward. If the one being fired is fired at a higher height then the only difference is that it will land father than the previous time it was launched.

Formulas

Δx=1/2(Vi+Vf)tΔx=Vit+1/2at²Vf=Vi+atVf^2=Vi²+2aΔx

Time is the connecting factor b/t horizontal and vertical motion

Problem Solving Steps

1. Draw Picture

2. Write Knowns

3. Identify Unknowns

4. Choose & Write equation to be used

5. Simp. Eq. by eliminating terms=0

6. Solve Eq. in terms of variables

7. Plug in #s & solve for Unknown

8. Ans. Given question & check ans.

Problem #1

The ball that was thrown horizontally from a cliff at a height of 25m and lands 8m from the base of the cliff. How fast was the ball going?

SOLVE

VERT HORIΔX 25m 8m

a 9.8m/s 0m/st 2.59s 2.59s

Vi 0 3.54m/s

Problem #2

• How far does a bullet land when shot horizontally at a height of 2m going at a speed of 20m/s?

Solve

Δxv=Vivtv+1/2avtv²T= √(Δx/.5a)T= √(2m/(9.8/2))T= .64s ------------------------------Δxh=Vihth+1/2ahth² a=0Δxh=Vihth

Δxh= 20m/s(.64s)Δxh= 12.8m The ball lands 12.8m away.

VERT HORIΔX 2m 12.8m

a 9.8m/s 0m/st .64s .64s

Vi 0 20m/s

Review Problems1. At the instant a ball is thrown horizontally over a level range,

a ball held at the side is dropped. If air-resistant is neglected which one strikes the ground first?

2. How far below an initial straight-line path will a horizontally fired projectile fall in 1sec?

3. Neglecting air resistance if a ball is thrown straight up at 20m/s, how fast will it be moving when you catch it?

4. At what point in the projectile speed is it at it’s minimum?

Answers

1. Both will hit at the same time.

2. 4.9m

3. 20m/s

4. At the top of it’s path where it’s changing

direction.