Answer:
Cool question! First step is to find the time taken to fall
57
m
, then to find the horizontal velocity needed to cover
24
m
in that time. In this case the answer is
7.0
m
s
−
1
.
Explanation:
This is a less typical projectile motion question, but it's still projectile motion. This means the horizontal and vertical directions can be considered separately. We assume that the initial vertical velocity,
u
y
=
0
m
s
−
1
, and we are trying to find the required initial horizontal velocity,
u
x
.
To find the time taken to fall
57
m
:
s
=
u
t
+
1
2
a
t
2
Since
u
=
0
, we can rearrange this to:
t
=
√
2
s
a
=
√
2
⋅
57
9.8
=
3.41
s
The horizontal velocity will be constant (ignoring air resistance), so to cover
24
m
in
3.41
s
will be given by:
v
=
s
t
→
u
x
=
24
3.41
=
7.0
m
s
−
1
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