The trajectory of a projectile can be described by the equations of motion. The basic formula for the trajectory of a projectile which is launched at some angle 𝚹 from the ground level with an initial velocity is,
has parametric equations:
1. Horizontal motion
2. Vertical motion
As,
x(t)= Horizontal position at time t
y(t)= Vertical position at time t
G is the gravitational acceleration
t= time in second
The trajectory can be written as one equation (removing \
t), by solving for t from the horizontal motion equation
Substitute this into the vertical motion equation
This is a parabolic equation, and is the trajectory of the projectile.
The maximum height H can be found from
The range R (horizontal distance travelled when it hits the ground) can be found as
It assumes no air resistance and that the launch and landing heights are equal.
Q1: Maximum Height
Known:
Initial velocity,
Launch angle,
Find:
Maximum height reached by the projectile.
Solution
Compute the vertical component of velocity
Applying maximum height formula
Given:
Initial velocity,
Launch angle,
Solution
Range formula
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The trajectory of a projectile can be described by the equations of motion. The basic formula for the trajectory of a projectile which is launched at some angle 𝚹 from the ground level with an initial velocity is,
has parametric equations:
1. Horizontal motion
2. Vertical motion
As,
x(t)= Horizontal position at time t
y(t)= Vertical position at time t
G is the gravitational acceleration
t= time in second
The trajectory can be written as one equation (removing \
t), by solving for t from the horizontal motion equation
Substitute this into the vertical motion equation
This is a parabolic equation, and is the trajectory of the projectile.
The maximum height H can be found from
The range R (horizontal distance travelled when it hits the ground) can be found as
It assumes no air resistance and that the launch and landing heights are equal.
Q1: Maximum Height
Known:
Initial velocity,
Launch angle,
Find:
Maximum height reached by the projectile.
Solution
Compute the vertical component of velocity
Applying maximum height formula
Given:
Initial velocity,
Launch angle,
Solution
Range formula
Other Related Sections
NCERT Solutions | Sample Papers | CBSE SYLLABUS| Calculators | Converters | Stories For Kids | Poems for Kids| Learning Concepts | Practice Worksheets | Formulas | Blogs | Parent Resource
Admissions Open for
An integral formula provides a method to evaluate the integral of a function, representing the area under the curve of that function or the accumulation of quantities.
Integral tables offer precomputed antiderivatives for various functions, simplifying the process of finding integrals for complex or unfamiliar functions.
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