Physics Unit 3: Projectile Motion
Holt Ch. 3.3
HW
Due
HW3-1
Fri 9/26
HW3-2
Mon 9/29
HW3-3
Wed 10/1
HW3-4
Thu 10/2
MQ 3
Fri 10/3
HW3-5
Mon 10/6
Assignment
Launched Horizontally
Read 93-96; (97) 3, 4; (99-bottom) 1; Supplemental Problem 1
r
Launched Horizontally, with v f
Supplemental Problem 2; (109) 31*, 32
*Do the problem as stated, but it’s no longer historically accurate. Aroldis Chapman
of the Cincinati Reds threw 105.1mph in 2010.
Launched at an Angle
Read 97-98; (99-top) 1*; (110) 34, 35; Supplemental Problem 3
*Find Δy when Δx=4.0m
r
Launched at an Angle, with v f
Do these problems: (110) 37; (112) 61; (99-bottom) 3.
r
After doing those problems,
for (110) 37, find v above the peak and as it lands.
r
Also, for (112) 61, find v f of the football.
Moodle Quiz 3 due by midnight Thursday night. This quiz is based on HW3-1
through HW3-4. Ten questions for ten points (5 × 1.5 + 5 × 0.5).
Launched at an Angle, with Δy a Given. Using Parametric Equations.
Supplemental Problems 4-6. Document the main parameters (v, θ, window, table)
that you put into the calculator.
Test: Tuesday 10/7 — a 3” × 5” note card is allowed
110 m/s
Supplemental Problems
1. Veronica the Stuntwoman is hanging off the bottom of an airplane
50 m
that is flying 50 m above the ground. The movie plot requires the
plane to be moving at 110 m/s. How far away from the landing
cushion should Veronica let go and become a projectile?
2. Look at the Sample Problem on page 96. Calculate the velocity vector
of the rock the instant before it hits the water surface. (You can use
any of the results given for this sample problem.)
3. A daredevil is shot out of a cannon at 45.0° above
horizontal with an initial speed of 25.0 m/s. A net is
positioned a horizontal distance of 50.0 m from the cannon.
At what height above the cannon should the net be placed
in order to catch the daredevil?
4. A cannon fires a cannonball from the edge of a 100-meter
cliff. If the initial velocity was 300 m/s and the launch
100 m
angle was 30° above the horizontal, how far away will the
cannonball land? Give 1-meter precision in your answer.
5. This is like problem 37 on page 110, but now the initial
velocity is 265 m/s and the mountain is an unknown
distance away. On its way down the projectile passes 84
meters above the top of the 1800-meter mountain. How far away is the mountain?
Assume θ still is 75°. Give 1-meter precision in your answer.
6. You’re trying to get the attention of your friend, who is up in her room, so you’re
tossing pebbles at the window. You consistently toss them at 15.20 m/s at 85.0°
above the horizontal, and the window is 10.00 meters above the ground. How far
away should you stand from the building so that you hit the window while the
pebble is on its way up? Give 1-cm precision in your answer.
?
?
?
Derivation of 2-D Equations of Motion
Common Substitutions
Completely General
Take the basic kinematic equations but make x and y components for
all vector quantities:
Δx =
1
2
(v
xi
)
+ vxf Δt
Δy =
1
2
(v
yi
Final Velocity Vector
)
+ v yf Δt
vxf = vxi + ax Δt
v yf = v yi + ay Δt
Δx = vxi Δt + 12 ax Δt 2
Δy = v yi Δt + 12 ay Δt 2
vxf2 = vxi2 + 2ax Δx
v yf2 = v yi2 + 2ay Δy
General Projectile Motion (launched at any angle)
Assumptions: ax=0 (which implies vxi=vxf so we can just call it vx) and ay=–g where g=9.81m/s2
(v
)
Δx = vx Δt
Δy =
vxf = vxi
v yf = v yi − gΔt
Δx = vx Δt
Δy = v yi Δt − 12 gΔt 2
vxf2 = vxi2
v yf2 = v yi2 − 2gΔy
1
2
yi
+ v yf Δt
• Note that the x-equations amount to just 1 equation: Δx = vx Δt
• Note that by making ay=–g we’re assigning up positive, down negative.
DO NOT use –9.81m/s2 for g since the negative sign is included explicitly in the equations.
Projectile Motion Launched Horizontally
Assumptions: ax=0 and ay=–g and vx=vi and vyi=0
Δx = vx Δt
Δy = 12 v yf Δt
v yf = − gΔt
Δy = − 12 gΔt 2
v = −2gΔy
2
yf
Common
rearrangement
Δt =
−2Δy
g