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Ch 3 Supplemental Questions
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Ch 3 Supplemental Questions
Due: 7:00pm on Wednesday, September 28, 2016
To understand how points are awarded, read the Grading Policy for this assignment.
Exercise 3.16
Description: On level ground a shell is fired with an initial velocity of v0 at phi above the horizontal and feels no
appreciable air resistance. (a) Find the horizontal and vertical components of the shell's initial velocity. (b) How long does
it...
On level ground a shell is fired with an initial velocity of 40.0 resistance.
at 70.0 ∘ above the horizontal and feels no appreciable air
m/s
Part A
Find the horizontal and vertical components of the shell's initial velocity.
Enter your answers numerically separated by a comma.
ANSWER:
, v0h v0v
, = = 13.7, 37.6 m/s Part B
How long does it take the shell to reach its highest point?
Express your answer using three significant figures.
ANSWER:
= 3.84
= t
Also accepted: = 3.83 , = 3.84
Part C
Find its maximum height above the ground.
Express your answer using three significant figures.
ANSWER:
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hmax
= = 72.1
Also accepted: = 72.0
, = 72.1
Part D
How far from its firing point does the shell land?
Express your answer using three significant figures.
ANSWER:
l
= 105
= Also accepted: = 105
, = 105
Part E
At its highest point, find the horizontal and vertical components of its acceleration.
Enter your answers numerically separated by a comma.
ANSWER:
ah
, av = 0, ­9.80 m/s2 Part F
At its highest point, find the horizontal and vertical components of its velocity.
Enter your answers numerically separated by a comma.
ANSWER:
vh
, vv = , = 13.7, 0 m/s Exercise 3.19
Description: In a carnival booth, you win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf
above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (the figure ). If
you toss the coin ...
In a carnival booth, you win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point
where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (the figure ). If you toss the coin with
a velocity of 6.4 m/s at an angle of 60 above the horizontal, the
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∘
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a velocity of 6.4 m/s at an angle of 60 above the horizontal, the
coin lands in the dish. You can ignore air resistance.
∘
Part A
What is the height of the shelf above the point where the quarter leaves your hand?
Express your answer using two significant figures.
ANSWER:
H
= 1.5 m Part B
What is the vertical component of the velocity of the quarter just before it lands in the dish?
Express your answer using two significant figures.
ANSWER:
vy
= ­0.89 m/s Exercise 3.25
Description: A jet plane comes in for a downward dive as shown in below. The bottom part of the path is a quarter circle
with a radius of curvature of 280 m . According to medical tests, pilots lose consciousness when they pull out of a dive at
an upward...
A jet plane comes in for a downward dive as shown in below. The bottom part of the path is a quarter circle with a radius of
curvature of 280 m . According to medical tests, pilots lose consciousness when they pull out of a dive at an upward
acceleration greater than 5.5g .
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Part A
At what speed (in m/s) will the pilot black out for this dive?
ANSWER:
= 120 m/s v
Also accepted: 123, 123, 120
Part B
At what speed (in mph) will the pilot black out for this dive?
ANSWER:
= 270 mph v
Also accepted: 275, 275, 270
Exercise 3.26
Description: A model of a helicopter rotor has four blades, each of length L from the central shaft to the blade tip. The
model is rotated in a wind tunnel at a rotational speed of f. (a) What is the linear speed of the blade tip? (b) What is the
radial...
A model of a helicopter rotor has four blades, each of length 3.10 m from the central shaft to the blade tip. The model is
rotated in a wind tunnel at a rotational speed of 530 rev/min .
Part A
What is the linear speed of the blade tip?
ANSWER:
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= 172 m/s = v
Part B
What is the radial acceleration of the blade tip expressed as a multiple of the acceleration of gravity, g?
ANSWER:
= 974 ⋅g = a
Problem 3.47
Description: In fighting forest fires, airplanes work in support of ground crews by dropping water on the fires. A pilot is
practicing by dropping a canister of red dye, hoping to hit a target on the ground below. (a) If the plane is flying in a
horizontal path...
In fighting forest fires, airplanes work in support of ground crews by dropping water on the fires. A pilot is practicing by
dropping a canister of red dye, hoping to hit a target on the ground below.
Part A
If the plane is flying in a horizontal path at an altitude of 84.0 m above the ground and with a speed of 71.0 m/s , at what
horizontal distance from the target should the pilot release the canister? Ignore air resistance.
Take free fall acceleration to be g.
ANSWER:
x
= = 294 m Problem 3.65
Description: A 76.0­kg boulder is rolling horizontally at the top of a vertical cliff that is 20 m above the surface of a lake,
as shown in the figure . The top of the vertical face of a dam is located 100 m from the foot of the cliff, with the top of the
dam...
A 76.0­kg boulder is rolling horizontally at the top of a vertical cliff that is 20 m above the surface of a lake, as shown in the
figure . The top of the vertical face of a dam is located 100 m from the foot of the cliff, with the top of the dam level with the
surface of the water in the lake. A level plain is 25 m below the top of the dam.
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Part A
What must be the minimum speed of the rock just as it leaves the cliff so it will travel to the plain without striking the dam?
Express your answer using two significant figures.
ANSWER:
v0x
= 49 m/s Part B
How far from the foot of the dam does the rock hit the plain?
Express your answer using two significant figures.
ANSWER:
L
= 50 m Problem 3.75
Description: Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia. Mia is running due north
with a speed of v_M. The velocity of the ball relative to Mia is v_b in a direction 30.0 degree(s) east of south. (a) What is
the magnitude of...
Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia. Mia is running due north with a speed of 6.80 ∘
m/s . The velocity of the ball relative to Mia is 4.30 m/s in a direction 30.0 east of south.
Part A
What is the magnitude of the velocity of the ball relative to the ground?
Express your answer to three significant figures and include the appropriate units.
ANSWER:
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= 3.75
= v
Part B
What is the direction of the velocity of the ball relative to the ground?
Express your answer to three significant figures and include the appropriate units.
ANSWER:
= 55.0
= θ
north of east
Problem 3.44
Description: A bird flies in the xy­plane with a velocity vector given by v_vec = ( alpha ­ beta t^2)i_unit + gamma t j_unit,
with alpha = 2.4 m/s, beta = 1.6 m/s^3, and gamma = 4.0 m/s^2. The positive y­direction is vertically upward. At t = 0 the
bird is at...
3
A bird flies in the xy­plane with a velocity vector given by v⃗ = (α − βt2 )^i + γt^
j , with α = 2.4 m/s, β = 1.6 m/s , and γ =
2
4.0 m/s . The positive y­direction is vertically upward. At t = 0 the bird is at the origin.
Part A
Calculate the position vector of the bird as a function of time.
→
Express your answer in terms of α, β, and γ . Write the vector r(t) in the form r(t)x , r(t)y , where the x and y
components are separated by a comma.
ANSWER:
, = ⃗ r (t)
Part B
Calculate the acceleration vector of the bird as a function of time.
→
Express your answer in terms of α, β, and γ . Write the vector a(t) in the form a(t)x , a(t)y , where the x and y
components are separated by a comma.
ANSWER:
a⃗ (t)
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Part C
What is the bird's altitude (y­coordinate) as it flies over x = 0 for the first time after t = 0?
Express your answer using two significant figures.
ANSWER:
y
= 9.0 m Problem 3.59
Description: A snowball rolls off a barn roof that slopes downward at an angle of 40 degree(s) . The edge of the roof is
14.0 m above the ground, and the snowball has a speed of 7.00 m/s as it rolls off the roof. Ignore air resistance.Assume
the coordinate...
A snowball rolls off a barn roof that slopes downward at an angle of 40 ∘ . The edge of the roof is 14.0 m above the ground,
and the snowball has a speed of 7.00 m/s as it rolls off the roof.
Ignore air resistance.
Assume the coordinate origin is at the point on the roof where the
snowball rolls off and that the positive x direction is to the right and
the positive y direction is upwards.
Part A
How far from the edge of the barn does the snowball strike the ground if it doesn't strike anything else while falling?
ANSWER:
x
= 6.93 m Part B
Draw x − t graphs for the motion in part A.
ANSWER:
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Part C
Draw y − t graphs for the motion in part A.
Plot points at t
= 0 s, t = 0.4 s, t = 0.8 s, t = 1.0 s, t = 1.3 s
.
ANSWER:
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Part D
Draw vx
−t
graphs for the motion in part A.
ANSWER:
Part E
Draw vy
−t
graphs for the motion in part A.
ANSWER:
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Part F
A man 1.9 m tall is standing 4.0 m from the edge of the barn. Will he be hit by the snowball?
ANSWER:
Yes
No
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