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a body takes t second to reach a maximum height 'h' m,when projected vertically upward from the groun.find the position of the body after t/2 seconds from the ground in terms of h. |
v=u+at……… (1). a=-g for a body projected vertically upward. v= 0 at the highest pt. Substituting
in (1), Time of
ascent, t=u/g. At t/2
seconds, t= u/2g. Substitute in
S=ut
– ½ gt2 = (u* u/2g) - ½ g*(u/2g) 2 = (u2/2g) – (u2/8g) = 3u2/8g………. (2). Maximum height, h = u2/2g [this is obtained by substituting a=-g and v= 0 in v2-u2=2aS]. u = root(2gh) substitute u in (2), S = 3*( root(2gh))2/8g = (3*2gh)/8g = ¾ h. |