150 Solutions Manual
Problem 2.102
Suppose that you can throw a projectile at a large enough
v0
so
that it can hit a target a distance
R
downrange. Given that you
know
v0
and
R
, determine the general expressions for the two
distinct launch angles
✓1
and
✓2
that will allow the projectile to
hit
D
. For
v0D30 m=s
and
RD70
m, determine numerical
values for ✓1and ✓2.
Solution
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 151
Problem 2.103
An alpine ski jumper can fly distances in excess of
100
m by using
his or her body and skis as a “wing” and therefore, taking advantage
of aerodynamic effects. With this in mind and assuming that a
ski jumper could survive the jump, determine the distance the
jumper could “fly” without aerodynamic effects, i.e., if the jumper
were in free fall after clearing the ramp. For the purpose of your
calculation, use the following typical data:
˛D11ı
(slope of
ramp at takeoff point
A
),
ˇD36ı
(average slope of the hill),
v0D86 km=h
(speed at
A
),
hD3
m (height of takeoff point with
respect to the hill). Finally, for simplicity, let the jump distance be
the distance between the takeoff point Aand the landing point B.
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
152 Solutions Manual
Problem 2.104
A soccer player practices kicking a ball from
A
directly into the goal (i.e., the ball does not bounce first)
while clearing a 6ft tall fixed barrier.
Determine the minimum speed that the player needs to give the ball to accomplish the task. Hint:
Consider the equation for the projectile’s trajectory of the form
yDC0CC1xCC2x2
, with the
y
axis
parallel to the direction of gravity, for the case in which the ball reaches the goal at its base. Solve this
equation for the initial speed
v0
as a function of the initial angle
✓
, and finally find
.v0/min
as you learned
in calculus. Don’t forget to check whether or not the ball clears the barrier.
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 153
Problem 2.105
A soccer player practices kicking a ball from
A
directly into the goal (i.e., the ball does not bounce first)
while clearing a 6ft tall fixed barrier.
Find the initial speed and angle that allow the ball to barely clear the barrier while barely reaching
the goal at its base. Hint: A projectile’s trajectory can be given the form
yDC1xC2x2
, where the
coefficients C1and C2can be found by forcing the parabola to go through two given points.
Solution
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permission of McGraw-Hill, is prohibited.
154 Solutions Manual
Problem 2.106
In a circus act a tiger is required to jump from point
A
to point
C
so that it goes through the ring of fire at
B
.Hint: A projectile’s trajectory can be given the form
yDC1xC2x2
, where the coefficients
C1
and
C2can be found by forcing the parabola to go through two given points.
Determine the tiger’s initial velocity if the ring of fire is placed at a distance
dD5:5
m from
A
.
Furthermore, determine the slope of the tiger’s trajectory as the tiger goes through the ring of fire.
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 155
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
156 Solutions Manual
Problem 2.107
In a circus act a tiger is required to jump from point
A
to point
C
so that it goes through the ring of fire at
B
.Hint: A projectile’s trajectory can be given the form
yDC1xC2x2
, where the coefficients
C1
and
C2can be found by forcing the parabola to go through two given points.
Determine the tiger’s initial velocity, as well as the distance
d
so that the slope of the tiger’s trajectory
as the tiger goes through the ring of fire is completely horizontal.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
158 Solutions Manual
Problem 2.108
A jaguar
A
leaps from
O
at speed
v0
and angle
ˇ
relative to the incline to attack a panther
B
at
C
.
Determine an expression for the maximum perpendicular height
hmax
above the incline achieved by the
leaping jaguar, given that the angle of the incline is ✓.
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 159
Problem 2.109
The jaguar
A
leaps from
O
at speed
v0
and angle
ˇ
relative to
the incline to intercept the panther
B
at
C
. The distance along
the incline from
O
to
C
is
R
, and the angle of the incline with
respect to the horizontal is ✓.
Determine an expression for
v0
as a function of
ˇ
for
A
to
be able to get from Oto C.
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.