Free-fall
What is the acceleration of an object in free fall on Earth?
9.81 m/s² downward.
A ball rolls off a table horizontally at 5.0 m/s. What determines how long it stays in the air?
The vertical distance to the ground.
What two components make up the initial velocity of a projectile?
Horizontal vx and vertical vy
What variable is shared by both horizontal and vertical motion in every projectile?
Time (t)
What is megameters (Mm) in meters (m)?
1 Mm = 106 m
A projectile is launched at 20 m/s and 30°. Find time to max height.
t = (vᵢ sin θ)/g = 1.02 s.
A ball is dropped from rest. How far does it fall in 2.0 s?
d = ½ g t² = 19.6 m.
A ball rolls off a 2.0 m high table. How long is it in the air?
t=0.64 s
A projectile is launched at 25 m/s and 30∘. Find the horizontal component of velocity.
vx=21.7 m/s
For a projectile at 20 m/s and 45°, find total flight time.
t = (2vᵢ sin θ)/g = 2.88 s.
The coefficient of friction for rubber on ice.
0.15
A diver jumps from 5.0 m with a horizontal velocity of 3.0 m/s. How far from the base does the diver land?
t = 1.01 s → dₓ = 3.0 m.
A ball is thrown upward at 15 m/s. How long until it returns to its starting height?
t = 2vᵢ / g = 3.06 s.
A ball goes off a 10.0 m cliff at 20.0 m/s. How far from the base does it land?
t=1.43 \ \text{s} \ d_x=28.6 \ \text{m}
A projectile is launched at 20 m/s and 45∘. What is its time to reach maximum height?
t=1.44 s
Find the horizontal range for a projectile at 20 m/s and 45°
vₓ = 14.1 m/s → R = vₓ t = 14.1(2.88) = 40.6 m.
The equation for impulse (J)
J=F_{\text{net}}t=Delta p
A projectile is launched from 15 m at 20 m/s and 40°. Find the total time before it hits the ground.
t = 3.4 s.
A rock is dropped from a cliff and hits the ground in 3.0 s. How high was the cliff?
d = ½ g t² = 44.1 m.
A projectile is launched horizontally at 12 m/s and lands 36 m away. Find the height of the cliff.
(Double)
d=44.1 m
A ball is launched at 15 m/s and 60∘. What is the total flight time?
t=2.65 s
A cannonball is launched at 30 m/s and 35°. Find its range.
R = (vᵢ² sin 2θ)/g = (900 × sin 70°)/9.81 = 85.5 m.
Energy of a photon (Ephoton)
E_{text{photon}}=h/f={hc}/lamda
Explain why projectile motion is modeled as two independent perpendicular motions.
Horizontal acceleration is zero, vertical acceleration is due to gravity—each axis is independent but shares the same time.
Describe how velocity and acceleration change as an object rises and falls.
Velocity decreases upward, zero at the top, increases downward; acceleration stays constant at 9.81 m/s² downward.
Explain why a ball dropped vertically and one rolled off the same table hit the ground at the same time.
They share the same vertical motion—both experience the same gravitational acceleration.
Compare what happens to time of flight, height, and range if launch angle increases while speed stays constant.
Time ↑, height ↑, range ↑ until 45°, then range ↓.
If two projectiles have the same speed, which pair of angles gives the same range?
(Double)
Complementary angles that add to 90° (e.g., 30° and 60°).
Planck's Constant
h=6.63*10-34 J*s
A baseball is hit from a 10 m platform at 25 m/s and 40°. How long is it in the air?
0 = 10m + 16.1 m/s t − 4.905 m/s2 t² → t = 3.82 s.