VDU_Physics_1_004.htm

# ## Free Fall and Motion under the Acceleration of Gravity

Javier Montenegro Joo

jmj@VirtualDynamicsSoft.com

Free Fall and Motion under the Acceleration of the Gravity

(1)  A 500kg bomb falls down from an airplane horizontally flying at  350 km/hr and at a height of 1000m. Determine: (a) Time to reach the ground. (b) Velocity at the moment of landing. (c) Distance travelled during the fifth sec. of the falling. (d) Velocity of the falling bomb during the fifth second of its falling. (e) Distance covered during the final sec. of the falling.

Solution.-

In this problem, neither the weight of the bomb nor the horizontal velocity of the airplane plays any role during the vertical falling of the bomb, which falls freely.  Since the bomb falls down from the airplane, its initial vertical velocity is zero. (2)  In a place where the acceleration of the gravity is 12 m/s2  , a rubber piece falls down to ground from a static helicopter at 800m height. Determine: (a) Time to reach ground. (b) Landing velocity. (c) Assuming the ground is elastic and the piece bounces with 100% of its landing velocity, find the height reached by the piece after bouncing.

Solution.- (3) A rubber ball of 2kg falls down from 100m height in a place where the acceleration of the gravity is 6 m/s2.   (a) Find the height that the ball reaches after bouncing on the ground with 40% of its landing velocity.

Solution.-

The first thing to do is to compute the landing velocity and, then take the 40% of this velocity to calculate the height reached when bouncing. Elastic-Collisions module of the PVL This is another ultra-interactive module included in the Physics Virtual Lab (PVL), which contains at least 201 Physics simulation modules.

(4) A Ping-Pong ball (60 gr) is launched vertically upwards with a velocity of 60 m/s. Determine: (a) After what time the ball is at 20 m height (b) the velocity of the ball when it is at 20 m height.

Solution.-

The ball will be two times at a height of  20 m, the first time when going upwards and, the second time when it is falling down. The velocities are equal at the same height, the only difference being its sign. (5) A 50gr stone is launched vertically upwards with a velocity of 20 m/s. Determine: (a) the maximum height attained by the stone (b) The flight time of the stone (c) After what time the stone will be at 15 m height.

Solution.-

A time equal to the flight time occurs when the stone returns to its initial position and as a consequence its displacement is zero. Note that since the stone is launched upwards, it will be twice at 15 m height, the first time when it goes upwards and the next time when it is returning to earth. (6) An 85 gr stone falls freely in a place where the acceleration of gravity is 15 m/s², traveling a distance of 217.50 m during the final second of its fall.    Determine: (a) The height the stone falls from. (b) The total falling time

Solution.-

Since the stone is not shot but it simply falls, its initial velocity is zero. The acceleration of the falling stone is that of the gravity, g.

If the total time of falling is  ' t ', then the total time minus 1, is  ' t-1 '. (7) An alien ball falls freely from a static UFO in the air and touches Earth 6 s later. Determine: (a) The height of the UFO when the ball falls down. (b) The landing speed of the ball (c) The height reached by the alien ball at bounce, if it is known that its bouncing speed is 75% of its landing speed.

Solution.- Book : Algorithms of  Digital Image Processing and Pattern Recognition

by  Javier Montenegro Joo (8) A 50 gr ball is launched vertically upwards with a velocity of 125 m/s. Determine (a) Ascending time of the ball (b) Maximum altitude reached by the ball (c) Altitude of the ball after 15 s (d) Altitude of the ball after 25.51 s (e) Landing velocity (f) Lapse of time the ball is in the air.

Solution.-  The Physics Virtual Lab (PVL) -created by Javier Montenegro Joo- currently includes at least 200  Physics simulation modules.

To know about the PVL click:     http://www.virtualdynamicssoft.com

 At a planet where the acceleration of the gravity is 12 m/s², a UFO is vertically ascending with a velocity of 150 m/s and when it is at 2500 m height, a 125 gr screw nut is released from its surface. Determine: (a) Distance the nut ascends before it starts to go downward. (b) During how long the nut goes upwards. (c) Time for the nut to fall down to earth from its highest position. (d) Landing velocity of the nut. (e) Flight-time of the nut.

Solution.- From the rooftop of a building of height Ho, a bullet is shot upwards with a velocity Voa.  Simultaneously another bullet is shot upwards from the base of the building with a velocity Vob, (Vob > Voa).  Determine the time for both bullets to meet and, their velocities at that moment.

Solution.- The VirtualDynamics Intelligencer Multidisciplinary Open Access Journal. Call for papers

http://www.virtualdynamicssoft.com/VD_Intelligencer/VDI_Main.htm

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 From the rooftop of a building of 100 m height, a bullet is shot upwards with a velocity of  125 m/s.  Simultaneously another bullet is shot upwards from the base of the building with a velocity of  250 m/s.  Determine the time for both bullets to meet, their velocities at that moment and their heights.

Solution.- 