Question

Define projectile motion ✔✔✔✔✅✅
& derivation



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Answer 1

Answer:

Projectile Motion.

When any object is thrown from horizontal at an angle θ except 90°, then the path followed by it is called trajectory, the object is called projectile and its motion is called projectile motion.

Derivation

derive the second equation, the change in angle with time?

dVdt=−gsinθ−gkV2(1)(1)dVdt=−gsin⁡θ−gkV2

dθdt=−gcosθV(2)(2)dθdt=−gcos⁡θV

dxdt=Vcosθ(3)(3)dxdt=Vcos⁡θ

dydt=Vsinθ(4)(4)dydt=Vsin⁡θ

where VV is the velocity of the point mass, θθ is the angle tangent to the trajectory of the point mass, mm is the mass of the particle, xx and yy are the Cartesian coordinates of the point mass, and −gkV2−gkV2 represents a drag force proportional to the square of the velocity.

Answer 2

Explanation:

Vo is the initial Velocity, sin θ is the component along y-axis, cos θ is the component along x-axis. Projectile Motion formula is used to find the distance, velocity and time taken in the projectile motion.

Important Points of Projectile Motion

The linear momentum at the highest point is mu cos Θ and the kinetic energy is (1/2)m(u cos Θ)2

After t seconds, the horizontal displacement of the projectile is x = (u cos Θ) t

After t seconds, the vertical displacement of the projectile is y = (u sin Θ) t – (1/2) gt2

The equation of the path of the projectile is y = x tan Θ – [g/(2(u2 cos Θ)2)]x2

The path of a projectile is parabolic.

At the lowest point, the kinetic energy is (1/2) mu2

At the lowest point, the linear momentum is = mu

Throughout the motion, the acceleration of projectile is constant and acts vertically downwards being equal to g.

The angular momentum of projectile = mu cos Θ × h where the value of h denotes the height.

The angle between the velocity and acceleration in the case of angular projection varies from 0 < Θ < 180 degrees.