Name: Parameters of Motion and Trajectory of Projectile
Uploaded: 2019-07-19
Duration: 10 min 13 s
Description: Mathematics is a great tool to analyse any motion. The expressions for the height, range and time of flight of projectile motion can be derived using math. L...

Question

Write the shape of the trajectory of a projectile in the mathematical form naming the terms in it.

Accepted Answer

The trajectory is the curved path of the object in respect to its motion along with the gravity. Furthermore, we also refer to it as projectile motion.It is a form of motion in which an object which is thrown in air travels a curved path under the action of gravity.

The trajectory formula help us find the gravity that acted on an object. Also, the trajectory has vertical (y) and horizontal (x) position components. Moreover, if we launch the projectile with an initial velocity v_o, at an angle θ from the horizontal plane. Then we can find the vertical position of the object from the horizontal position using this formula

Vertical position = (horizontal position) (tangent of launch angle) – $\frac{(a c c e l e r a t i o n d u e t o g r a v i t y) {(h o r i z o n t a l p o s i t i o n)}^{2}}{2 {(i n i t i a l v e l o c i t y)}^{2} {(\cos i n e o f l a u n c h a n g l e)}^{2}}$

$y = x \tan θ - \frac{g x^{2}}{2 {v_{o}}^{2} \cos^{2} θ}$

y = refers to the vertical position of the object in meters
x = refers to the horizontal position of the object in meters
v_o = refers to the initial velocity of the object combined with meter per second
g = refers to the acceleration due to gravity that is 9.80 m/s²
θ =refers to the initial angle from the horizontal plane in degrees or radians.

Write the shape of the trajectory of a projectile in the mathematical form naming the terms in it.

Important Questions on Projectile Motion

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