SOLUTION: Marian, who is standing on her balcony, is surprised by a pigeon and throws a flowerpot up in the air at 2.1 m/s. It takes 3.0 s for the flowerpot to smash to the ground. The flowe

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Marian, who is standing on her balcony, is surprised by a pigeon and throws a flowerpot up in the air at 2.1 m/s. It takes 3.0 s for the flowerpot to smash to the ground. The flowe      Log On

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Question 1076627: Marian, who is standing on her balcony, is surprised by a pigeon and throws a flowerpot up in the air at 2.1 m/s. It takes 3.0 s for the flowerpot to smash to the ground. The flowerpot experiences acceleration due to gravity of 9.81 m/s [down].

a) How high is Marian’s balcony?

b) How fast was the flowerpot moving just before it smashed to the ground?

My Solutions:

a) displacement = 1/2 (acceleration x time^2) + (v1 x time)

displacement = 1/2 (9.81 m/s [down] x 9) + (2.1 x 3)

d = 1/2 (88.29) + 6.3

d = 44.145 + 6.3 = 50.445

so the balcony is approximately 50.5 meters tall


b) velocity = acceleration x time

Vf = (9.8 m/s^2 [down]) x 3.0 s
= 29.4 m/s

Feedback and corrections appreciated.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29+=+-%281%2F2%29%2A9.81t%5E2+%2B+2.1t+%2B+h%5B0%5D+
When it hits the ground, +h%28t%29+=+0+
+0+=+-%281%2F2%29%2A9.81t%5E2+%2B+2.1t+%2B+h%5B0%5D+
It takes +t+=+3+ sec to hit the ground, so
+0+=+-%281%2F2%29%2A9.81%2A3%5E2+%2B+2.1%2A3+%2B+h%5B0%5D+
+44.145+-+6.3+=+h%280%29+
+h%280%29+=+37.845+ m
The balcony is 37.845 m high
------------------------------
+h%5E2%283%29+=+%28-1%2F2%29%2A9.81t+%2B+2.1+
+h%5E2%283%29+=+%28-1%2F2%29%2A9.81%2A3+%2B+2.1+
+h%5E2%283%29+=+-14.7+%2B+2.1+
+h%5E2%283%29+=+-12.6+
The flowerpot was moving 12.6 m/sec in
the down direction just before it hit ground
-----------------------------------------
Here is the graph:

To check this I'll find +h%5Bmax%5D+
+t%5Bmax%5D+=+-b%2F%282a%29+
+t%5Bmax%5D+=+-2.1%2F%282%2A%28-4.9%29%29+
+t%5Bmax%5D+=+.2143+ sec
and
+h%5Bmax%5D+=+-%281%2F2%29%2A9.81%2A.2143%5E2+%2B+2.1%2A.2143+%2B+37.845+
+h%5Bmax%5D+=+-%281%2F2%29%2A9.81%2A.0459+%2B+.45+%2B+37.845+
+h%5Bmax%5D+=+-%281%2F2%29%2A.45+%2B+.45+%2B+37.845+
+h%5Bmax%5D+=+.225+%2B+37.845+
+h%5Bmax%5D+=+38.07+ m
This looks about right
Definitely get a 2nd opinion on this!