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PROBLEM 11.106
At halftime of a football game souvenir balls are
thrown to the spectators with a velocity v0.
Determine the range of values of v0 if the balls are
to land between Points B and C.
SOLUTION
The motion is projectile motion. Place the origin of the xy-coordinate system at ground level just below Point A.
The coordinates of Point A are 00
0, 2m.xy
The components of initial velocity are 00
() cos40m/s
vv
0
2
00
1.5 10sin 35 7.2358 m
16.1915 21.1365 m
cos 40
2 16.1915 tan 40 7.2358 1.3048 s
4.905
21.1365 16.199 m/s
1.3048
y
vt
tt
vv
PROBLEM 11.106 (Continued)
PROBLEM 11.107
A basketball player shoots when she is 16 ft from the
backboard. Knowing that the ball has an initial velocity v
0
at an
angle of 30° with the horizontal, determine the value of v
0
when
d is equal to (a) 9 in., (b) 17 in.
SOLUTION
12
3
PROBLEM 11.108
A tennis player serves the ball at a height h 2.5 m with an initial velocity of v0 at an angle of 5° with the
horizontal. Determine the range for which of v0 for which the ball will land in the service area which extends
to 6.4 m beyond the net.
SOLUTION
The motion is projectile motion. Place the origin of the xy-coordinate system at ground level just below the
0
2
00
12.2 12.2466 m
cos 5
2.5 12.2 tan 5 0.914 0.32517 s
4.905
12.2466 37.66 m/s
0.32517
vt
tt
vv
PROBLEM 11.108 (Continued)
PROBLEM 11.109
The nozzle at A discharges cooling water with an initial
velocity v
0
at an angle of 6° with the horizontal onto a grinding
wheel 350 mm in diameter. Determine the range of values of
the initial velocity for which the water will land on the
grinding wheel between Points B and C.
SOLUTION
0
00
cos 6 2 cos 6
PROBLEM 11.109 (Continued)
2
1
22
(9.81)(0.050388)
PROBLEM 11.110
While holding one of its ends, a worker lobs a coil of rope over the
lowest limb of a tree. If he throws the rope with an initial velocity v
0
at an angle of 65° with the horizontal, determine the range of values
of v
0
for which the rope will go over only the lowest limb.
SOLUTION
PROBLEM 11.110 (Continued)
PROBLEM 11.111
The pitcher in a softball game throws a ball with an initial velocity v
0
of 72 km/h at an angle
with the
horizontal. If the height of the ball at Point B is 0.68 m, determine (a) the angle
, (b) the angle
that the
velocity of the ball at Point B forms with the horizontal.
SOLUTION
First note
2
cos
PROBLEM 11.111 (Continued)
PROBLEM 11.112
A model rocket is launched from Point A with an initial velocity v0 of
75 m/s. If the rocket’s descent parachute does not deploy and the
rocket lands a distance d 100 m from A, determine (a) the angle
that v0 forms with the vertical, (b) the maximum height above Point A
reached by the rocket, and (c) the duration of the flight.
SOLUTION
PROBLEM 11.112 (Continued)
PROBLEM 11.113
The initial velocity
v
0
of a hockey puck is 105 mi/h. Determine (a) the largest value (less than 45°) of
the angle
for which the puck will enter the net, (b) the corresponding time required for the puck to reach
the net.
front enter enter
2
2
818
(154 sin ) 77 cos 2 77 cos
32
16 tan 5929 cos
g
g
PROBLEM 11.113 (Continued)
1sec 1 tan
PROBLEM 11.114
A worker uses high-pressure water to clean the inside of a long drainpipe. If the water is discharged with an
initial velocity
v
0
of 11.5 m/s, determine (a) the distance d to the farthest Point B on the top of the pipe that the
worker can wash from his position at A, (b) the corresponding angle
.
PROBLEM 11.114 (Continued)
PROBLEM 11.115
An oscillating garden sprinkler which
discharges water with an initial velocity
v
0
of 8 m/s is used to water a vegetable
garden. Determine the distance d to the
farthest Point B that will be watered and
the corresponding angle
when (a) the
vegetables are just beginning to grow,
(b) the height h of the corn is 1.8 m.
SOLUTION
max
PROBLEM 11.115 (Continued)
PROBLEM 11.116*
A nozzle at A discharges water
with an initial velocity of 36 ft/s at
an angle with the horizontal.
Determine (a) the distance d to the
farthest point B on the roof that the
water can reach, (b) the
corresponding angle Check
that the stream will clear the edge
of the roof.
.
