Physics 151 – Kinematics Problem Solving Example

brontidegrrrMechanics

Nov 14, 2013 (3 years and 10 months ago)

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Physics 151


Kinematics Problem Solving Example
-
KEY


Problem:

On October 9, 1992, a 27
-
pound meteorite struck a car in
Peekskill, NY, leaving a dent 22 cm deep in the trunk. If the meteorite struck
the car with a speed of 550 m/s, what was the magnit
ude of its deceleration,
assuming it to be constant?


Draw a simple diagram
showing the
meteor’s starting
and ending points

and

the
origin and direction of increase of your
coordinate system.










Write out the values of the known
and unknown

variabl
es.








v
0

= 550 m/s






a = ?


v = 0 m/s


x = 0.22 m


Wha
t kinematics variable(s) is/are not involved
?


t

Which kinematic equation does that suggest that you should use?

2 2
0
2
v v ax
 


Solve that kinematic equation for the variable of in
terest?




Plug in the known values and solve for the desired quantity?






But

since we are asked for magnitude, the minus sign is not needed
, thus the answer is


6.9 x 10
5

.


2 2
0
2 2
0
2 2
0
2
2
2
v v ax
v v ax
v v
a
x
 
 




2
2
2 2
5
0
2
0 550
6.9 10
2 2 0.22
m m
v v
m
s s
a
x m s
   

   

   
    
Original top

of car trunk

Final top

of car trunk

meteor

v = 0 m/s

v
0

= 550 m/s

x = 0.22 m

X

Are the
units on your answer correct? How do you kn
ow? Yes, I know because all my numbers
are in SI units and my unit analysis gave me these units. I also know because they are
[length]/[time]
2
, which are the correct dimensions for acceleration.


Does you
r

answer appear reasonable?

Hard to say
--

we shou
ld certainly expect a large
value of acceleration since the meteor is brought to a stop very quickly.




2. A model rocket rises with constant acceleration to a height of 3.2 m, at wh
ich point is speed is
26.0 m/s. [Make sure you show your work for all
parts of this question.]


(a) How much time does it take for the rocket to reach this height?

Let “x” be in the vertical
direction

with “up” being positive
.


Note that since the rocket has a constant acc
eleration
and the initial velocity is zero,

the ave
rage
velocity must be half of the final velocity.
So I would write,









While
your textbook writes:






(b) What was the magnitude of the rocket’s acceleration?









(c) Find the hei
ght and speed of the rocket 0.075

s after launch.






0
m m
0
s s
2( )
2(3.2 m– 0 m)
0.25 s
0 26.0
x x
t
v v

  


m
s
3.2 m
0.25
13.0
x vt
x
t s
v

  
m m
2
0 s s
26.0 – 0
110 m s
0.246 s
v v
a
t

  