Physics Lord

Free Fall Motion

•       An object is said to be in the state of free fall if gravity is the only force acting on it

•       Assumption

•       The motion is along the vertical

•       Gravity is the only force

•       Acceleration  is always 9.8m/s²

•       Air resistance is neglected

•       Scenarios

•       Dropped

•       V_iy = 0

•       Acceleration is 9.8m/s² as it falls

•       Thrown Downward

•       Non zero initial velocity

•       Acceleration is 9.8m/s² as it falls

•       Thrown upward

•       Non zero initial velocity

•       Slow down on its way up

•       Zero velocity at the peak

•       Accelerate at 9.8m/s²

Example

•       A ball was dropped from a very high building

–      A. How far below its dropping point will it have a speed of 1960m/s^{2 .} How many seconds after it was dropped will have this speed?   Ans.

–      B. What is the speed of the ball and how far is it below its dropping point 5.0s after it was dropped?

–      C^. How many seconds since the ball was dropped will it be 3,136m below its dropping point? What will be the velocity at the moment?

–      What is the acceleration at the peak

–      F. What is the acceleration 38.0sec after it was fired

–      G. What is the velocity 50s after it was fired?

–      I.  At what time is it 3926 m above the ground?

A ball is dropped from rest from the top of a building. Find:

a)      The instantaneous velocity of the ball after 6 sec.

b)      How the ball fell.

c)       The average velocity up to that point.

PROJECTILE MOTION

Example

                Volleyball, cannon , baseball

Path of the projectile: Like a parabola

Acceleration

Since there is only acceleration in the vertical direction, the velocity in the horizontal direction is constant, being equal to V_i cos θ. The vertical motion of the projectile is the motion of a particle during its free fall. Here the acceleration is constant, being equal to .^[1] The components of the acceleration are:

a_x = 0

a_y  = -9.8m/s²   or  32.2 ft/s²

^Note: Acceleration is entirely vertical along the path of projectile

     

The horizontal component of the velocity of the object remains unchanged throughout the motion. The vertical component of the velocity increases linearly, because the acceleration due to gravity is constant. The accelerations in the  and  directions can be integrated to solve for the components of velocity at any time ,

Note: Velocity is entirely horizontal at the peak of the projectile

          Velocity remain the same at the entire horizontal.

Initial Velocity (Vi) is the beginning of the projectile motion,

Angle (θ)  - angle of elevation with respect to horizontal ground

There are two components of Velocity

Vix = Vi cos θ    (horizontal Component)

Viy = Vi sin θ    (Vertical component)

Maximum Height (dymax) – highest altitude the object reach during the projectile motion

            Vy = 0

dymax =  V_iyt + ½ gt²

dymax = Vf_y – ½ gt²

2gdymax = Vf_y² – Vi_y²

2dymax = (Vf_y + Vi_y)t

 Time to reach the maximum height  (t)

      t =   (Vf_y – Vi _y)/g

TOTAL TIME OF FLIGHT  (T)  = 2 x t

MAXIMUM RANGE – Rmax 

            Rmax  =  Vix T

Example:

An arrow leaves a bow at 30m/s at angle of 30° from the horizontal.

Solve first for the Horizontal and Vertical Component of initial velocity

Viy = ?

Vix =?

Then solve for Max. Height  (dymax)   Answer: 11.5m

Then solve for time at Max height : answer: 1.5s

Since max height is at halfway of the projectile, therefore

            Total time of flight (T) = 2t     Answer: 3.0s

Solve for Max range:

            R =  V_ix t   Answer: 78m

2. Supposed that a coin rolls off the edge of a table 1.5m high at a horizontal speed of 1.0m/s

a. Find the time it would take before the coin land in the floor

b. Find the Maximum range

Since Vi is already in horizontal, Vix = 1.0m/s

To solve for the time: use 

dymax =  V_iyt + ½ gt²    Answer: 0.55s

Given:

     dymax =  -15m (since it is downward)

     g = -9.8m/s²

                           

Solve for Maximum Range:

R =  V_ix t        Answer: 0.55m