Hellow Dear students…
Here we have discussed the relative projectile motion of two particles…In which we have discussed collision time , collision coordinate, and if there are not collide than what would be the minimum distance between those two particles….
WATCH TILL THE END DEAR STUDENTS FOR THE CLEAR CONCEPT AND IDEA…..
HERE THE LINKS OF GROUPS…
It is the best example to understand motion in a plane. If we project a particle obliquely from the
surface of earth, as shown in the figure below, then it can be considered as two perpendicular 1D
motions – one along the horizontal and other along the vertical.
Assume that effect of air friction and wind resistance are negligible and value of ‘acceleration due to
Take point of projection as origin and horizontal and vertical direction as +ve X and Y-axes, respectively.
For X-axis For Y – axis
= u cosθ, uy
= u sinθ
= 0, ay
= – g,
= u cosθ, and v
= u sinθ – gt, and
x = u cosθ × t y = u sinθ t –
It is clear from above equations that horizontal component of velocity of the particle remains constant
while vertical component of velocity is first decreasing, gets zero at the highest point of trajectory and
then increases in the opposite direction. At the highest point, speed of the particle is minimum.
The time, which projectile takes to come back to same (initial) level is called the time of flight (T).
At initial and final points, y = 0,
So u sinθ t –
gt2 = 0
⇒ t = 0 and t
So, T =
Range (R) The horizontal distance covered by the projectile during its motion is said to be range of the
Speed, kinetic energy, momentum of the particle initialy decreases in a projectile motion and attains a
minimum value (not equal to zero) and then again increases.
θ is the angle between
v and horizontal which decreases to zero. (at top most point) and again
increases in the negative direction
Projectile motion is a form of motion experienced by an object or particle (a projectile) that is thrown near the Earth’s surface and moves along a curved path under the action of gravity only (in particular, the effects of air resistance are assumed to be negligible). This curved path was shown by Galileo to be a parabola. The study of such motions is called ballistics, and such a trajectory is a ballistic trajectory. The only force of significance that acts on the object is gravity, which acts downward, thus imparting to the object a downward acceleration. Because of the object’s inertia, no external horizontal force is needed to maintain the horizontal velocity component of the object. Taking other forces into account, such as friction from aerodynamic drag or internal propulsion such as in a rocket, requires additional analysis. A ballistic missile is a missile only guided during the relatively brief initial powered phase of flight, and whose subsequent course is governed by the laws of classical mechanics.
Ballistics (gr. βάλλειν (‘ba’llein’), “to throw”) is the science of mechanics that deals with the flight, behavior, and effects of projectiles, especially bullets, unguided bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance.
Trajectories of a projectile with air drag and varying initial velocities
The elementary equations of ballistics neglect nearly every factor except for initial velocity and an assumed constant gravitational acceleration. Practical solutions of a ballistics problem often require considerations of air resistance, cross winds, target motion, varying acceleration due to gravity, and in such problems as launching a rocket from one point on the Earth to another, the rotation of the Earth. Detailed mathematical solutions of practical problems typically do not have closed-form solutions, and therefore require numerical methods to address.