VDU_Physics_1_004  
 

 

Solved University-Physics Problems

Physics 1.- Mechanics:   Free Fall 

Javier Montenegro Joo

jmj@VirtualDynamics.Org

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  Free Fall  
     
 

(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.

 
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(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.

 
     
 

(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.

 
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(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/sē, 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.-

 
     
     
     
 

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