Physics
Kinematics
Vertical Motion in Projectile Motion
Class 11
⚡ Quick Summary
The vertical part of projectile motion is just like throwing something straight up in the air. Gravity slows it down as it goes up, it stops at the top, and then gravity pulls it back down.
v_y = u sinθ - gt
The vertical motion of a projectile is identical to the motion of a particle projected vertically upward with an initial speed of u sinθ, where u is the initial velocity and θ is the angle of projection.
Horizontal Motion in Projectile Motion
Class 11
⚡ Quick Summary
The horizontal motion of a projectile is super simple! It just keeps moving at the same speed in the same direction because there's no force (like gravity) pulling it sideways (we're ignoring air resistance).
x = u cosθ * t
The horizontal motion of the particle is identical to a particle moving horizontally with uniform velocity u cosθ, where u is the initial velocity and θ is the angle of projection.
Time of Flight
Class 11
⚡ Quick Summary
Time of flight is simply the total time the projectile stays in the air.
T = 2u sinθ / g
The time of flight (T) is the total time for which the projectile remains in the air, returning to the same vertical level from which it was launched.
Range
Class 11
⚡ Quick Summary
The range is how far the projectile travels horizontally before it hits the ground.
R = u² sin(2θ) / g
The range (OB) is the horizontal distance traveled by the projectile during its flight.
Maximum Height
Class 11
⚡ Quick Summary
The maximum height is the highest vertical point the projectile reaches during its flight.
H = u² sin²(θ) / (2g)
At the maximum height (A), the vertical component of the projectile's velocity is zero.
Time to Reach Maximum Height
Class 11
⚡ Quick Summary
It takes the same amount of time to go up to the highest point as it does to come back down.
t = u sinθ / g
The time taken to reach the maximum height is exactly half the total time of flight.
Change of Frame
Class 11
⚡ Quick Summary
How we see motion depends on where *we're* standing (our frame of reference). If we're moving, things look different than if we're standing still.
Not explicitly defined in the text, but implies transformations between coordinate systems will affect values of position, velocity, and acceleration.
The position, velocity, and acceleration of a particle depend on the frame of reference chosen by the observer. Different frames of reference may be moving relative to each other.
Scalar
11
⚡ Quick Summary
A quantity that has magnitude only.
N/A
Scalars are physical quantities that are completely described by their magnitude. Examples include mass, time, and temperature.
Vector
11
⚡ Quick Summary
A quantity that has both magnitude and direction.
N/A
Vectors are physical quantities that have both magnitude and direction. Examples include displacement, velocity, and force. Vectors can be added using graphical or analytical methods.
Velocity
11
⚡ Quick Summary
The rate of change of displacement.
velocity = displacement / time
Velocity is a vector quantity that describes the rate at which an object changes its position. It includes both speed and direction.
Average Velocity
11
⚡ Quick Summary
Total displacement divided by total time.
Average velocity = Total displacement / Total time
Average velocity is the total displacement divided by the total time taken for the motion.
Instantaneous Velocity
11
⚡ Quick Summary
Velocity at a specific instant in time.
v = lim (Δt→0) Δx/Δt
Instantaneous velocity is the velocity of an object at a particular moment in time. It is the limit of the average velocity as the time interval approaches zero.