A particle is moving vertically upward and reaches the maximum height H in T seconds. The height of the particle at any time t ( t > T) will be?
A: #H  g( t  T )^2#
B: #g(t  T)^2#
C: #H  1/2g(t  T)^2#
D: #g/2(t  T)^2#
A:
B:
C:
D:
1 Answer
Aug 4, 2017
(C)
Explanation:
When the particle is at its maximum height, its motion after this point is analogous to that of a particle dropped from rest at a certain height
With that being said, we can use the kinematics equation
#ul(y = y_0 + v_(0y)t  1/2g t^2#
where

the initial height
#y_0# is the maximum height#H# 
the initial velocity
#v_(0y)# is#0# (equivalent to being dropped from rest) 
#t# represents all times after#T# , i.e. is equivalent to the expression#tT#
Since the initial velocity is
#ul(y = y_0  1/2g t^2#
Plugging in values from above yields
#color(red)(ulbar(stackrel(" ")(" "y = H  1/2g(tT)^2" "))#