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Bio-mechanics problem of vertical Jump of a person from standing position.
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CALCULATING HEIGHT OF A VERTICAL JUMP
Vertical jump
A vertical jump is the act of raising one's center of gravity higher in the vertical plane
Solely with the use of one's muscles It is a measure of how high an individual
can elevate off the ground (jump) from a standstill.
Centre of gravity of person
•Point at which all weight of person is acting
•It is at 56% height of person approx
Consider a simple jump
Positions attained during a standing vertical jump
Centre of gravity lowers by a distance c when person bent for exerting force
Force is produced as reaction to force exerted on surface by legs,which pull body upwards against gravity
H is height is height attained by jumper
Calculating height attained
Calculating height attained•We will assume that same force is being exerted by legs on ground
•As a result of this force equal and opposite force is exerted by surface
•Two forces ,weight in downward direction & reaction force in upward, are acting
•Net upward force is F-W until feet leave ground,i-e through distance c
•Acceleration at this stage is
a=( F-W)/m = (F-W)/(W/g)
Calculating height attained
a=( F-W)/m = (F-W)/(W/g) Where W is the weight of jumper G is gravitational acceleration A consideration of forces acting
A consideration of forces acting on earth
•As seen equal force is being exerted on earth
•But mass of earth is so large that its acceleration due to jump is negligible
Calculating height attained
Veocity is given by
Putting value of acceleration calculated and considering v initial= 0
Calculating height attained
Only force acting is gravity W Which produces downward acceleration –g After reaching max H, just before falling
back V is zero , v initial for this part is V
Which when is inserted in equation below
Becomes
From this height of jump is
Calculating height attained
Calculating height attained
In Good jump F=2W c is propotional to height of legs For average person c=60cm
Height can be also calculated by
Energy consideration Work done on jumper is equal to force
and distance c This work is converted to kinetic energy At full height velocity is zero K.E is fully converted to P.E as center of
mass of jumper is raised to height(c+h)
From law of conservation of energy Workdone on body= P.E at maximum
height
Height is
Energy consideration
Applications
Height of vertical jump is increased in sports
Mainly o basket ball, o volley ball o and gymnastics
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