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Solved: During launches, rockets often discard unneeded
Chapter 2, Problem 93P(choose chapter or problem)
Problem 93P
During launches, rockets often discard unneeded parts. A certain rocket starts from rest on the launch pad and accelerates upward at a steady 3.30 m/s2. When it is 235 m above the launch pad, it discards a used fuel canister by simply disconnecting it. Once it is disconnected, the only force acting on the canister is gravity (air resistance can be ignored). (a) How high is the rocket when the canister hits the launch pad, assuming that the rocket does not change its acceleration? (b) What total distance did the canister travel between its release and its crash onto the launch pad?
Questions & Answers
QUESTION:
Problem 93P
During launches, rockets often discard unneeded parts. A certain rocket starts from rest on the launch pad and accelerates upward at a steady 3.30 m/s2. When it is 235 m above the launch pad, it discards a used fuel canister by simply disconnecting it. Once it is disconnected, the only force acting on the canister is gravity (air resistance can be ignored). (a) How high is the rocket when the canister hits the launch pad, assuming that the rocket does not change its acceleration? (b) What total distance did the canister travel between its release and its crash onto the launch pad?
ANSWER:Solution 93P
Step 1 of 2:
a)Speed of the rocket rocket when canister is released
It starts from rest ,so initial velocity,=0
y-= 235 m
=
+2
(y-
)
=2
(y-
)
=
=
=39.4 m/s
For the motion of caister after it is reached,
=39.4 m/s
=0
y-= -235 m
=
+2
(y-
)
(y-)=
t+
-235=(39.4)t-4.9
The quadratic formula gives t = 12 s the the motion of the rocket during this 12 s
(y-)=235+39.4
12.5+
(3.30)
=945 m
(y-
)=
=
=79.2 m
After its release canister move upwards 79.2 m to its maximum height then back down 79.2 m to 235 m to the ground. The total distance travelled is 393 m