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 heightH -
the initial velocity
v_(0y) is0 (equivalent to being dropped from rest) -
t represents all times afterT , i.e. is equivalent to the expressiont-T
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(t-T)^2" ")|)