Definitions [12]
Define the following term:
Free fall
A path of free fall is the term used to describe the movement of an object solely under the influence of gravity.
The motion of an object in which the position of a particle varies only in terms of distance along a straight line is called Rectilinear Motion.
The magnitude of projection velocity — which, with a fixed projection angle, shows the length of trajectory or range — is called the projection speed.
The acceleration acting on an object undergoing uniform circular motion, which always acts on the object along the radius towards the centre of the circular path, is called centripetal acceleration.
The total maximum horizontal distance travelled by a projectile from the point of projection to the point where it hits the ground is called the horizontal range (R).
The maximum vertical height reached by the projectile — i.e., the distance travelled along the vertical (y) direction up to the highest point — is called the maximum height (H).
The time taken by the projectile to travel from the point of projection to the maximum height is called the time of ascent (tA).
An object in flight after being thrown with some velocity that follows a curved path under the action of gravity is called a projectile.
OR
A body in free fall which is subjected to the force of gravity and air resistance only — which refers to the motion of bodies flung into the air — is called a projectile.
The total time for which the projectile remains in the air — from the moment it is projected to the moment it returns to the same level — is called the time of flight (T).
The time taken by the projectile to travel from the maximum height back to the ground is called the time of descent (tD).
The path followed by a projectile is called its trajectory.
The direction of projection with respect to the horizon which determines the shape of trajectory (vertical → vertical, oblique → parabolic, horizontal → half parabolic) is called the projection angle.
Formulae [1]
| Quantity | Formula |
|---|---|
| Position after time t | x = (u cos θ)t, y = (u sin θ)t − \[\frac {1}{2}\]gt2 |
| Equation of trajectory | y = x tan θ − \[\frac {g}{2u^2 cos^2 θ}\] ⋅ x2 |
| Maximum height | H = \[\frac {u^2 sin^2 θ}{2g}\] |
| Time of flight | T = \[\frac {2u sin θ}{g}\] |
| Horizontal range | R = \[\frac {u^2 sin 2θ}{g}\] |
| Maximum range | Rmax = \[\frac {u^2}{g}\] at θ = 45° |
| Velocity after time ttt | vx = u cos θ, vy = u sin θ − gt |
| Speed | v = \[\sqrt {v_x^2+v_y^2}\] |
Key Points
- Horizontal range is maximum at 45° and reduces for any other angle of projection.
- A projectile has two simultaneous independent motions — constant horizontal and gravity-driven vertical.
- The path is a symmetric parabola — equal time up and down, equal speed at the same height.
Important Questions [26]
- Find the Co-ordinate of the Centroid of the Area as Shown in the Given Figure.
- The Position Vector of a Particle Which Moves in the X-y Plane is Given by 𝒓̅ = (3t3-4t2)𝒊̅ + (0.5t4)𝒋̅
- Two Balls Having 20kg and 30 Kg Masses Are Moving Towards Each Other with Velocities of 10 M/S and 5 M/S Respectively as Shown in the Figure.
- The V-x Graph of a Rectilinear Moving Particle is Shown. Find the Acceleration of the Particle at 20m,80 M and 200 M.
- A Bar 2 M Long Slides Down the Plane as Shown.The End a Slides on the Horizontal Floor with a Velocity of 3 M/S.Determine the Angular Velocity of Rod Ab and the Velocity of End
- A 500 N Crate Kept on the Top of a 15° Sloping Surface is Pushed Down the Plane with an Initial Velocity of 20m/S. If μS = 0.5 and μK = 0.4, Determine the Distance Travelled by the Block and T
- Derive the Equation of Path of a Projectile and Hence Show that Equation of Path of Projectile is a Parabolic Curve.
- Particle is Moving in X-y Plane and It’S Position is Defined by ¯ R = ( 3 2 T 2 ) ¯ L + ( 2 3 T 3 ) ¯¯¯ J Find Radius of Curvature When T=2sec.
- P a Force of 100 N Acts at a Point P(-2,3,5)M Has Its Line of Action Passing Through Q(10,3,4)M. Calculate Moment of this Force About Origin (0,0,0).
- A Circle of Diameter 1.5 M is Cut from a Composite Plate.Determine the Centroid of the Remaining Area of Plate.
- A Rod Ab Has an Angular Velocity of 2 Rad/Sec,Counter Clock Wise as Shown.End C of Rod Bc is Free to Move on a Horizontal Surface.Determine: (1)Angular Velocity of Rod Bc (2)Velocity of C
- Velocity-time Diagram for a Particle Travelling Along a Straight Line is Shown in Figure 10. Draw Acceleration-time and Displacement-time Diagram for the Particle. Also Find Important Values of
- A 75kg Person Stands on a Weighing Scale in an Elevator. 3 Seconds After the Motion Starts from Rest, the Tension in the Hoisting Cable Was Found to Be 8300n. Find the Reading of the Scale, in
- Two springs, each having stiffness of 0.6N/cm and length 20 cm are connected to a ball B of weight 50N. The initial tension developed in each spring is 1.6N.
- Two Balls, a (Mass 3kg) and B (Mass 4kg), Are Moving with Velocities 25 M/S and 40 M/S Respectively (Refer Figure 15). before Impact, the Direction of Velocity of Two Balls Are 300 and 500 with the L
- Blocks P1 and P2 Are Connected by Inextensible String.Find Velocity of Block P1,If It Falls by 0.6 M Starting from Rest.The Co-efficient of Friction is 0.2.The Pulley is Frictionless.
- Co-ordinate Distance Are in M Units for the Space Frame in Figure. There Are 3 Members Ab,Ac and Ad.There is a Force W=10 Kn Acting at a in a Vertically Upward Direction.
- A Glass Ball is Dropped on a Smooth Horizontal Floor from Which It Bounces to a Height of 9m.On the Second Bounce It Rises to a Height of 6 M.From What Height Was the Ball Dropped
- Angular Velocity of Connector Bc is 4 R/S in Clockwise Direction.What is the Angular Velocities of Cranks Ab and Cd?
- The acceleration time diagram for a linear motion is shown. Construct velocity time diagram and displacement time diagram for the motion assuming that the motion starts
- A Particle Moves in X-y Plane with Acceleration Components Ax = -3m/S2 and Ay = -16t M/S2. If Its Initial Velocity is V0 = 50m/S Directed at 350 to the X–Axis, Compute the Radius of Curvature of the
- A Particle Falling Under Gravity Travels 25 M in a Particular Second. Find the Distance Travelled by It in the Next 3 Seconds.
- From (V-t) Diagram Find (1) Distance Travelled in 10 Second.(2) Total Distance Travelled in 50 Second.(3) Retardation
- Determine the Speed at Which the Basket Ball at a Must Be Thrown at an Angle 30o So that If Makes It to the Basket at B. Also Find at What Speed It Passes Through the Hoop.
- Figure Shows a Collar B Which Moves Upwards with Constant Velocity of 1.5 M/S.At the Instant When θ=50o.Determine :(I)The Angular Velocity of Rod Pinned at B and Freely Resting at a Against 25o
- Find an Expression for Maximum Range of a Particle Which is Projected with an Initial Velocity of ‘U’ Inclined at an Angle of ‘β’ with the Horizontal.
