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Quiz 1
Question 1
A 4
th
July rocket accelerates from rest uniformly and vertically up from the ground.
After 5 seconds the rocket’s stick drops off and moves independently, hitting the ground
6 seconds later.
What was the acceleration of the rocket?
How high was the rocket
when the stick fell off?
Take g=9.8m/s
2
and ignore air resistance.
We will use the physics of linear motion with constant acceleration
Choose a coordinate system with y=0 at the ground and y increasing upwards
Initial conditions
for the rocket are y
0r
=0, v
0r
=0.
The position of the rocket (y
r
) after time t is given by
y
r
=y
0r
+v
0r
t+1/2at
2
=1/2at
2
The velocity of the rocket is
v
r
=v
0r
+at
At the time t
1
when the stick falls off
y
r1
=1/2at
1
2
v
r1
=at
1
The stick now falls under gravity, its position y
s
time t after falling off is given by
y
s
= y
s1
+v
s1
t1/2gt
2
At the point where the stick falls off
y
s1
=y
r1
,
v
s1
=v
r1
When the stick hits the ground after time t
2
, y
s
=0
0=1/2at
1
2
+at
1
t
2
1/2gt
2
2
We know everything except a
a(1/2t
1
2
+t
1
t
2
)=1/2gt
2
2
2
2
2
0.5 9.8 6
176.4
4.2
/
(0.5 5
5 6)
42.5
am
s
××
==
=
×+×
The height of the rocket was y
r1
=1/2at
1
2
=0.5x4.15x25=
52.0m
Both results to 2 significant figures
Check for reasonableness?
Acceleration is 0.5g, OK, height is typical rocket height, OK
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 Fall '08
 Marshak
 Acceleration

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