2020HW1soln
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School
North Carolina State University *
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Course
208
Subject
Aerospace Engineering
Date
Dec 6, 2023
Type
Pages
7
Uploaded by Amonanny
MAE 208 Engineering Dynamics
Dr. Saul
Due January 22 2020
Total Possible Points: 30
Check your work using the informationprovided. Boxyour answer to the underlined question.
- 2 -
K. Saul MAE 208
1.
Measurements of a shot recorded on a videotape during a basketball game are shown. The ball
passed through the hoop, just barely clearing the hands of player B who attempted to block it.
Neglecting the size of the ball (i.e. treat it like a particle), determine the magnitude v
A
ofits initial
velocity. W
h
a
t
i
s
t
h
e
h
e
i
g
h
t
h
o
f
t
h
e
b
a
l
l
w
h
e
n
i
t
p
a
s
s
e
s
o
v
e
r
p
l
a
y
e
r
B
?
CHECK: v
A
= 36.7 ft/s
SOLUTION: h = 11.5 ft. y positions of points A, B, and C will depend on the origin of your
coordinate system. The solution puts it on the ground just below the ball at position A. Youmay have
chosen to place it at the ball at position A. In your problemyou needed to INCLUDE A DRAWING
THAT HAS A COORDINATE SYSTEM ORIGIN INDICATED.
- 3 -
K. Saul MAE 208
2.
A baseballis thrown downward from a 60-ft tower with an initial speed of 20 ft/s. Determine the
speed at which it hits the ground. W
h
a
t
i
s
t
h
e
t
i
m
e
o
f
t
r
a
v
e
l
?
CHECK: v
2
= 65.3 ft/s
SOLUTION:
t = 1.4 s
Note that in this solution, the origin of the coordinate system was at the top of the tower and positive
s-axis was down. If your origin was at the base of the tower with the positive direction up, the initial
velocity would need to be -20 m/s, the initial position would be 60 ft and the final position would be 0
ft. Acceleration would also be negative (instead of positive). IT IS ESSENTIAL THAT YOU
INCLUDE A DRAWING WITH YOUR SOLUTION THAT INDICATES THE LOCATION
AND DIRECTION OF YOUR COORDINATE SYSTEM.
Also note that this problem could have been solved by using the constant acceleration equation for
position. This would require using the quadratic equation to solve for the two possible values of t and
choosing the most appropriate (i.e. the positive) one. The constant acceleration equation for velocity
would then be used to find the final velocity when the baseball hit the ground.
I chose this problem to point out that it is sometimes easier to use that “third” equation that does not
have time in it. I often forget about it as an option and I thought youmight too.
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- 4 -
K. Saul MAE 208
3.
A car starts from rest and travels along a straight road with the
given velocity profile. Determine total distance traveled until the
car stops. C
o
n
s
t
r
u
c
t
t
h
e
s
-
t
a
n
d
a
-
t
g
r
a
p
h
s
.
CHECK: total distance = 1350 m
SOLUTION:
- 5 -
K. Saul MAE 208
4.
The car travels along the curve having a radius of 300 m. Ifits speed is uniformly increased from 12
m/s to 24 m/s in 2 s, what is the normal compoenent of the acceleration of the car at the instant its
speed is 20 m/s? D
e
t
e
r
m
i
n
e
t
h
e
m
a
g
n
i
t
u
d
e
o
f
i
t
s
a
c
c
e
l
e
r
a
t
i
o
n
.
CHECK: a
n
= 1.33 m/s
2
SOLUTION:
a = 6.14 m/s
2
- 6 -
K. Saul MAE 208
5.
A particle travels along a portion of the “four-leaf rose” which is defined by the equation r = (5cos 2
θ
)
m. If the angular velocity of the radial coordinate line is d
θ
/dt = 3t
2
rad/s, where t is in seconds,
determine the radial and t
r
a
n
s
v
e
r
s
e
c
o
m
p
o
n
e
n
t
s
of the particle’s velocity and acceleration at the instant
θ
= 30
o
. At t=0,
θ
=0
o
.
CHECK: v
r
= -16.9 m/s, a
r
= -89.4 m/s
2
,
SOLUTION:
v
θ
= 4.87 m/s, a
θ
= -53.7 m/ s
2
Note that in this problem, theta is given in radians, so youmust convert before you use the 30
o
.
(Also
be sure to use your calculator consistently with whatever values you are using.) Also note the need to
use the CHAIN RULEmultiple times in this problem. Whenever you are taking a derivative relating r,
v, and a, that derivative is respect to TIME. If there are any variables that are not time, but are a
function of time, like theta, youmust use the chain rule to differentiate properly.
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- 7 -
K. Saul MAE 208
6.
If block A is moving downward with a speed of 3 ft/s while C is moving upward at 4 ft/s, determine
the speed of block B. W
h
a
t
d
i
r
e
c
t
i
o
n
i
s
i
t
m
o
v
i
n
g
(
u
s
e
y
o
u
r
d
a
t
u
m
s
a
n
d
a
n
s
w
e
r
t
o
g
e
t
h
e
r
t
o
a
n
s
w
e
r
t
h
i
s
)
?
CHECK: v
B
= 0.5 ft/s
SOLUTION:
It is moving downwards.
You must measure the position of the blocks from a FIXED POINT. Your drawing must indicate the
fixed point you chose, and thus the positive direction of the coordinates you are defining. You then need
to be sure that you use the velocities given to you in the problem in a manner consistent with the signs of
your coordinate system.