Projectile Motion
Trajectory equation, time of flight, maximum height and range. (Physics › Kinematics, NEET UG syllabus.)
What is Projectile Motion?
Two-dimensional motion under gravity alone; horizontal velocity stays constant while vertical velocity changes at g = 9.8 m/s2
Key formula / rule: Time of flight and height
Key points
- Resolve projectile motion into independent horizontal and vertical components and use range, height and time of flight
Common exam trap
Taking velocity as zero at maximum height
Definitions
- Name
Projectile motion
- Definition
Two-dimensional motion under gravity alone; horizontal velocity stays constant while vertical velocity changes at g = 9.8 m/s2
- Name
Key idea
- Definition
The components are independent; at the highest point the vertical velocity is zero but the speed is u cos(θ)
- Name
Exam insight
- Definition
Range is maximum at an angle of projection of 45 degrees, Rmax = u2/g; complementary angles give equal range
- Name
Worked example
- Definition
u = 20 m/s at 45 degrees: T ~ 2.9 s, H ~ 10.2 m, R ~ 40.8 m
Learning objectives
Resolve projectile motion into independent horizontal and vertical components and use range, height and time of flight
Formulae
- Name
Time of flight and height
- Expression
T = 2 u sin(θ)/g; H = u2 sin2(θ)/(2g)
- Name
Horizontal range
- Expression
R = u2 sin(2 θ)/g
Common mistakes
Taking velocity as zero at maximum height
Using g in the horizontal direction, where acceleration is zero
Keywords
projectile motion
angle of projection
range
maximum height
time of flight
trajectory
motion in a plane
45 degrees
Practice preview
For a given initial speed, at what angle of projection will the horizontal range of a projectile be maximum?…
easy
A projectile is fired with an initial velocity of 20 m/s at an angle of 30 degrees above the horizontal. Calculate its time of flight. (Take g = 10 m/s^2)…
medium
A particle is projected from the ground with an initial velocity of 20 m/s at 30 degrees above the horizontal. What is the magnitude of its velocity after 1 second? (Take g = 10 m/s^2)…
hard