Electromagnetism, Properties Of Waves, Motion, Gases & The Kinetic Theory Worksheet With Answers Page 18
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36The equations
Remember that displacement, velocity and acceleration are all ‘vectors’ – you
must be aware of their directions.
In the last example this wasn’t a problem since the direction of movement was in the same
direction as gravity (downwards). However, you must be prepared for examination questions
that involve using the correct direction, as shown in the next example :
Example 2
A ball is thrown vertically upwards with a speed of 7.2 m/s.
2
Taking the acceleration as 9.81 m/s
, calculate,
(a) the time it takes to reach its maximum height
We start by deciding on a ‘positive’ direction. So, let’s take upwards as positive.
Next, lets insert all given values :
x
At first glance it seems we’re stuck as we need 3 values but
= ?
only have 2 ! However, since the question asks for the time it
+
u
=
7.2 m/s
takes to reach the greatest height, we know that, at this
v
= ?
instant, the final velocity, v is zero !
-
2
a
=
9.81 m/s
t
= ?
Also notice that the acceleration is negative (since it’s always
downwards)
The only equation containing ‘u’, ‘v’, ‘a’ and ‘t’ (i.e.not ‘x ’) is :
v = u + at
Re-arranging
t = v – u = 0 - 7.2 = + 0.73 s
a
- 9.81
(b) the maximum height reached by the ball
We now know 4 values :
Since 4 of the 5 quantities are known, we can use any equation
x
= ?
containing ‘x’:
u
= + 7.2 m/s
v
= 0
x = ut + ½ a t
2
a
= - 9.81
t
= 0.73 s
-
x = (7.2 x 0.73) + (0.5 x
2
9.81 x 0.73
)
-
x =
5.256
2.614
x =
2.64 m
Notice that if we had NOT taken direction into account, the acceleration value would have
+
been positive, and the answer would have been “5.256
2.614”, which is incorrect !!
18
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