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

1 Answer
Aug 4, 2017

(C) "height" = H - 1/2g(t-T)^2

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 H and time T.

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 t-T

Since the initial velocity is 0, that leaves us with

ul(y = y_0 - 1/2g t^2

Plugging in values from above yields

color(red)(ulbar(|stackrel(" ")(" "y = H - 1/2g(t-T)^2" ")|)