hello, here is my question.....please answer step by step if possible...thanks........As a newspaper delivery boy Jason needs to know his projectile motion to throw a paper horozontally from a height of 1.40 m to a door that is 13.5 m away what must the papers velocity be for it to reach the door? :?
velocity question help
- Thread starter shawnarae
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Hello, shawnarae!
Here is my "without tears" explanation.
\(\displaystyle \text{The paper is launched horizontally at }v\text{ meters per second.}\)
\(\displaystyle \begin{array}{ccccc}\text{The horizontal displacement is:} & x \;=\; vt \\ \text{The vertical displacement is:} & y \;=\; 1.4 - 4.9t^2 \end{array}\)
\(\displaystyle \text{The paper hits the ground when }y \,=\,0\!:\)
. . \(\displaystyle 1.4 - 4.9t^2 \:=\:0 \quad\Rightarrow\quad 4.9t^2 \,=\,1.4 \quad\Rightarrow\quad t^2 \,=\,\tfrac{2}{7} \quad\Rightarrow\quad t \:=\:\sqrt{\tfrac{2}{7}}\)
\(\displaystyle \text{During that time, the paper has moved 1.5 m horizontally: }\:x \,=\,13.5\)
. . \(\displaystyle vt \,=\,13.5 \quad\Rightarrow\quad v\sqrt{\tfrac{2}{7}} \:=\:13.5 \quad\Rightarrow\quad v \:=\:13.5\sqrt{\tfrac{7}{2}} \;=\;25.2561\hdots\)
\(\displaystyle \text{To reach the door, the paper's velocity must be about 25.3 m/sec (or more).}\)
Here is my "without tears" explanation.
\(\displaystyle \text{The paper is launched horizontally at }v\text{ meters per second.}\)
\(\displaystyle \begin{array}{ccccc}\text{The horizontal displacement is:} & x \;=\; vt \\ \text{The vertical displacement is:} & y \;=\; 1.4 - 4.9t^2 \end{array}\)
\(\displaystyle \text{The paper hits the ground when }y \,=\,0\!:\)
. . \(\displaystyle 1.4 - 4.9t^2 \:=\:0 \quad\Rightarrow\quad 4.9t^2 \,=\,1.4 \quad\Rightarrow\quad t^2 \,=\,\tfrac{2}{7} \quad\Rightarrow\quad t \:=\:\sqrt{\tfrac{2}{7}}\)
\(\displaystyle \text{During that time, the paper has moved 1.5 m horizontally: }\:x \,=\,13.5\)
. . \(\displaystyle vt \,=\,13.5 \quad\Rightarrow\quad v\sqrt{\tfrac{2}{7}} \:=\:13.5 \quad\Rightarrow\quad v \:=\:13.5\sqrt{\tfrac{7}{2}} \;=\;25.2561\hdots\)
\(\displaystyle \text{To reach the door, the paper's velocity must be about 25.3 m/sec (or more).}\)
D
Deleted member 4993
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That's more than 55 mph - will get you speeding ticket in residential roads......
mmm4444bot
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shawnarae said:
It doesn't work that way, at this help site, Shawnrae.
You show us your answers first; we will then provide something for comparison.
Okay my apologies, here is what I have:
Distance refers to how much ground an object covers during it's motion it is a scalar quantity. Displacement refers to how far out of place an object is or how far away from the starting point. Displacement is a vector quantity.
Speed is a scalar quantity that refers to how fast an object is moving.
Velocity is a vector quantity, and it can be described as the rate in which an object changes position.
They are all related to one another.
Distance refers to how much ground an object covers during it's motion it is a scalar quantity. Displacement refers to how far out of place an object is or how far away from the starting point. Displacement is a vector quantity.
Speed is a scalar quantity that refers to how fast an object is moving.
Velocity is a vector quantity, and it can be described as the rate in which an object changes position.
They are all related to one another.
mmm4444bot
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shawnarae said:
You've correctly identified the scalars versus vectors.
If you feel that the exercise wants you to also say something about why each is either scalar or vector, then the difference between their definitions is that a vector has direction and a scalar does not.
Displacement and velocity are both vectors because they each provide a direction in addition to a numerical size. Scalars are just numbers, no direction.
You could think of distance as the absolute value of displacement; in other words, the magnitude of the length regardless of any direction toward which it might be pointing (positive or negative or other).
You could think of speed as the absolute value of velocity; that is, the magnitude of the velocity vector while completely ignoring any directional information.
I sometimes think of the displacement vector as a directed distance and the velocity vector as a directed speed.
D
Deleted member 4993
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Speed is the magnitude part of the velocity vector.
There is a good discussion regarding distance and displacement at:
http://physics.info/displacement/
There is a good discussion regarding distance and displacement at:
http://physics.info/displacement/