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