derive the relation between max height and range
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The range and the maximum height of the projectile does not depend upon its mass. Hencerange and maximum height are equal for all bodies that are thrown with the same velocity and direction. The horizontalrange d of the projectile is the horizontal distance it has traveled when it returns to its initial height( ).
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First, there are some essential equation regarding one-dimension motion with constant acceleration:
v=v0+atv=v0+at (1)
x=x0+v0t+12at2x=x0+v0t+12at2 (2)
v2−v20=2asv2−v02=2as (3)
(where v is the final velocity, v0v0 is the initial velocity, x is the displacement, s is the distance the object travels along the direction of acceleration)
(All this set of equations can be proved with simple calculus)
v=v0+atv=v0+at (1)
x=x0+v0t+12at2x=x0+v0t+12at2 (2)
v2−v20=2asv2−v02=2as (3)
(where v is the final velocity, v0v0 is the initial velocity, x is the displacement, s is the distance the object travels along the direction of acceleration)
(All this set of equations can be proved with simple calculus)
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