Additional Sample Problems with solutions
1. A body is projected directly downward from an elevated point with an initial velocity of
s
m
/
10
.
If the height h above the ground is
(
29
meters
t
t
h
10
5
500
2


=
where
t
is the time in
seconds after the instant it was projected, find (a) the velocity and (b) the acceleration of the
body 3 seconds after it was projected.
Sol’n:
10
10


=
=
t
dt
h
d
v
substituting
3
=
t
we have
(
29
s
m
s
m
v
/
40
/
10
30

=


=
The negative velocity means it is moving downwards.
2
/
10
s
m
dt
v
d
a

=
=
, again the negative accelerations means it is directed towards the
ground.
2. A boy on the ground throws a ball vertically upward with an initial speed of
s
m
/
49
.
The
path of the ball is described by the equation
2
2
8
.
9
49
t
t
h

=
, where
h
is the height in meters
above the ground and
t
is the elapsed time after the ball is thrown.
Find the time when the
ball reaches its maximum height.
Sol’n:
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 Spring '11
 darp
 Acceleration, Velocity, initial velocity, dt, Dh, VDT

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