تكلم مع الذكاء الاصطناعي
Deck 12: Section 3: Vector-Valued Functions
ملء الشاشة (f)
سؤال
The quarterback of a football team releases a pass at a height of 8 feet above the playing field, and the football is caught by a receiver 38 yards directly downfield at a height of 4 feet. The pass is released at an angle of 
with the horizontal. Find the speed of the football when it is released. Round your answer to three decimal places.
A) 33.169 feet per second
B) 59.366 feet per second
C) 19.462 feet per second
D) 118.732 feet per second
E) 190.165 feet per second
with the horizontal. Find the speed of the football when it is released. Round your answer to three decimal places.A) 33.169 feet per second
B) 59.366 feet per second
C) 19.462 feet per second
D) 118.732 feet per second
E) 190.165 feet per second
سؤال
A baseball, hit 9 feet above the ground, leaves the bat at an angle of 
and is caught by an outfielder 9 feet above the ground and 500 feet from home plate. What is the initial speed of the ball? Round your answer to two decimal places.
A) 31.62 ft/sec
B) 126.49 ft/sec
C) 189.74 ft/sec
D) 158.11 ft/sec
E) 63.25 ft/sec
and is caught by an outfielder 9 feet above the ground and 500 feet from home plate. What is the initial speed of the ball? Round your answer to two decimal places.A) 31.62 ft/sec
B) 126.49 ft/sec
C) 189.74 ft/sec
D) 158.11 ft/sec
E) 63.25 ft/sec
سؤال
The position vector 
describes the path of an object moving in space. Find the velocity 
of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the velocity of the object.A)
B)
C)
D)
E)
سؤال
A baseball, hit 5 feet above the ground, leaves the bat at an angle of 
and its caught by an outfielder 5 feet above the ground and 500 feet from home plate. How high does the ball rise? Round your answer to the nearest integer.
A) 77 feet
B) 10 feet
C) 167 feet
D) 118 feet
E) 23 feet
and its caught by an outfielder 5 feet above the ground and 500 feet from home plate. How high does the ball rise? Round your answer to the nearest integer.A) 77 feet
B) 10 feet
C) 167 feet
D) 118 feet
E) 23 feet
سؤال
The position vector 
describes the path of an object moving in space. Find the velocity 
of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the velocity of the object.A)
B)
C)
D)
E)
سؤال
The position vector 
describes the path of an object moving in space. Find the speed 
of the object.
A) 21
B)
C)
D) 149
E)
describes the path of an object moving in space. Find the speed of the object.A) 21
B)
C)
D) 149
E)
سؤال
Use the given acceleration function and initial conditions to find the position at time t = 3. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The position vector 
describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point 
.
A)
B)
C)
D)
E)
describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point .A)
B)
C)
D)
E)
سؤال
Use the given acceleration function and initial conditions to find the position at time t = 1. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
A baseball player at second base throws a ball 87 feet to the player at first base. The ball is thrown 5 feet above the ground with an initial velocity of 50 miles per hour and at an angle of 
above the horizontal. At which height does the player at first base catch the ball? Round your answer to three decimal places.
A) 7.576 feet
B) 6.676 feet
C) 5.476 feet
D) 6.076 feet
E) 5.576 feet
above the horizontal. At which height does the player at first base catch the ball? Round your answer to three decimal places.A) 7.576 feet
B) 6.676 feet
C) 5.476 feet
D) 6.076 feet
E) 5.576 feet
سؤال
The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 76 yards directly downfield at a height of 2 feet. The pass is released at an angle of 
with the horizontal. Find the maximum height of the football. Round your answer to one decimal place.
A) -377.3 feet
B) -374.2 feet
C) -425.8 feet
D) -528.2 feet
E) -583.0 feet
with the horizontal. Find the maximum height of the football. Round your answer to one decimal place.A) -377.3 feet
B) -374.2 feet
C) -425.8 feet
D) -528.2 feet
E) -583.0 feet
سؤال
Use the given acceleration function and initial conditions to find the position at time t = 1. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The position vector 
describes the path of an object moving in space. Find the speed 
of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the speed of the object.A)
B)
C)
D)
E)
سؤال
Find the vector-valued function for the path of a projectile launched at a height of 20 feet above the ground with an initial velocity of 50 feet per second at an angle of 35 degrees above the horizontal. Use a graphing utility to graph the path of the projectile and confirm your selection. Let i be the unit vector in the horizontal direction and j the unit vector in the vertical direction.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine the maximum height of a projectile fired at a height of 6 feet above the ground with an initial velocity of 700 feet per second and at an angle of 
above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.
A) 14,289.757 feet
B) 14,292.757 feet
C) 7,146.378 feet
D) 7,149.378 feet
E) 14,298.757 feet
above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.A) 14,289.757 feet
B) 14,292.757 feet
C) 7,146.378 feet
D) 7,149.378 feet
E) 14,298.757 feet
سؤال
The quarterback of a football team releases a pass at a height of 8 feet above the playing field, and the football is caught by a receiver 46 yards directly downfield at a height of 4 feet. The pass is released at an angle of 
with the horizontal. Find the time in seconds the receiver has to reach the proper position after the quarterback releases the football. Round your answer to one decimal place.
A) 7.0 seconds
B) 2.3 seconds
C) 4.1 seconds
D) 0.7 second
E) 1.1 seconds
with the horizontal. Find the time in seconds the receiver has to reach the proper position after the quarterback releases the football. Round your answer to one decimal place.A) 7.0 seconds
B) 2.3 seconds
C) 4.1 seconds
D) 0.7 second
E) 1.1 seconds
سؤال
The position vector 
describes the path of an object moving in space. Find the acceleration 
of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the acceleration of the object.A)
B)
C)
D)
E)
سؤال
Determine the range of a projectile fired at a height of 5 feet above the ground with an initial velocity of 1000 feet per second and at an angle of 
above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.
A) 15,627.500 feet
B) 8,137.843 feet
C) 31,252.187 feet
D) 31,254.999 feet
E) 16,268.138 feet
above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.A) 15,627.500 feet
B) 8,137.843 feet
C) 31,252.187 feet
D) 31,254.999 feet
E) 16,268.138 feet
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ملء الشاشة (f)
Deck 12: Section 3: Vector-Valued Functions
1
The quarterback of a football team releases a pass at a height of 8 feet above the playing field, and the football is caught by a receiver 38 yards directly downfield at a height of 4 feet. The pass is released at an angle of with the horizontal. Find the speed of the football when it is released. Round your answer to three decimal places.
A) 33.169 feet per second
B) 59.366 feet per second
C) 19.462 feet per second
D) 118.732 feet per second
E) 190.165 feet per second
with the horizontal. Find the speed of the football when it is released. Round your answer to three decimal places.A) 33.169 feet per second
B) 59.366 feet per second
C) 19.462 feet per second
D) 118.732 feet per second
E) 190.165 feet per second
59.366 feet per second
2
A baseball, hit 9 feet above the ground, leaves the bat at an angle of and is caught by an outfielder 9 feet above the ground and 500 feet from home plate. What is the initial speed of the ball? Round your answer to two decimal places.
A) 31.62 ft/sec
B) 126.49 ft/sec
C) 189.74 ft/sec
D) 158.11 ft/sec
E) 63.25 ft/sec
and is caught by an outfielder 9 feet above the ground and 500 feet from home plate. What is the initial speed of the ball? Round your answer to two decimal places.A) 31.62 ft/sec
B) 126.49 ft/sec
C) 189.74 ft/sec
D) 158.11 ft/sec
E) 63.25 ft/sec
126.49 ft/sec
3
The position vector describes the path of an object moving in space. Find the velocity of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the velocity of the object.A)
B)
C)
D)
E)
4
A baseball, hit 5 feet above the ground, leaves the bat at an angle of and its caught by an outfielder 5 feet above the ground and 500 feet from home plate. How high does the ball rise? Round your answer to the nearest integer.
A) 77 feet
B) 10 feet
C) 167 feet
D) 118 feet
E) 23 feet
and its caught by an outfielder 5 feet above the ground and 500 feet from home plate. How high does the ball rise? Round your answer to the nearest integer.A) 77 feet
B) 10 feet
C) 167 feet
D) 118 feet
E) 23 feet
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5
The position vector describes the path of an object moving in space. Find the velocity of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the velocity of the object.A)
B)
C)
D)
E)
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6
The position vector describes the path of an object moving in space. Find the speed of the object.
A) 21
B)
C)
D) 149
E)
describes the path of an object moving in space. Find the speed of the object.A) 21
B)
C)
D) 149
E)
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7
Use the given acceleration function and initial conditions to find the position at time t = 3.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
The position vector describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point .
A)
B)
C)
D)
E)
describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point .A)
B)
C)
D)
E)
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9
Use the given acceleration function and initial conditions to find the position at time t = 1.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
A baseball player at second base throws a ball 87 feet to the player at first base. The ball is thrown 5 feet above the ground with an initial velocity of 50 miles per hour and at an angle of above the horizontal. At which height does the player at first base catch the ball? Round your answer to three decimal places.
A) 7.576 feet
B) 6.676 feet
C) 5.476 feet
D) 6.076 feet
E) 5.576 feet
above the horizontal. At which height does the player at first base catch the ball? Round your answer to three decimal places.A) 7.576 feet
B) 6.676 feet
C) 5.476 feet
D) 6.076 feet
E) 5.576 feet
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11
The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 76 yards directly downfield at a height of 2 feet. The pass is released at an angle of with the horizontal. Find the maximum height of the football. Round your answer to one decimal place.
A) -377.3 feet
B) -374.2 feet
C) -425.8 feet
D) -528.2 feet
E) -583.0 feet
with the horizontal. Find the maximum height of the football. Round your answer to one decimal place.A) -377.3 feet
B) -374.2 feet
C) -425.8 feet
D) -528.2 feet
E) -583.0 feet
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12
Use the given acceleration function and initial conditions to find the position at time t = 1.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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13
The position vector describes the path of an object moving in space. Find the speed of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the speed of the object.A)
B)
C)
D)
E)
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14
Find the vector-valued function for the path of a projectile launched at a height of 20 feet above the ground with an initial velocity of 50 feet per second at an angle of 35 degrees above the horizontal. Use a graphing utility to graph the path of the projectile and confirm your selection. Let i be the unit vector in the horizontal direction and j the unit vector in the vertical direction.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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15
Determine the maximum height of a projectile fired at a height of 6 feet above the ground with an initial velocity of 700 feet per second and at an angle of above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.
A) 14,289.757 feet
B) 14,292.757 feet
C) 7,146.378 feet
D) 7,149.378 feet
E) 14,298.757 feet
above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.A) 14,289.757 feet
B) 14,292.757 feet
C) 7,146.378 feet
D) 7,149.378 feet
E) 14,298.757 feet
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16
The quarterback of a football team releases a pass at a height of 8 feet above the playing field, and the football is caught by a receiver 46 yards directly downfield at a height of 4 feet. The pass is released at an angle of with the horizontal. Find the time in seconds the receiver has to reach the proper position after the quarterback releases the football. Round your answer to one decimal place.
A) 7.0 seconds
B) 2.3 seconds
C) 4.1 seconds
D) 0.7 second
E) 1.1 seconds
with the horizontal. Find the time in seconds the receiver has to reach the proper position after the quarterback releases the football. Round your answer to one decimal place.A) 7.0 seconds
B) 2.3 seconds
C) 4.1 seconds
D) 0.7 second
E) 1.1 seconds
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17
The position vector describes the path of an object moving in space. Find the acceleration of the object.
A)
B)
C)
D)
E)
describes the path of an object moving in space. Find the acceleration of the object.A)
B)
C)
D)
E)
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18
Determine the range of a projectile fired at a height of 5 feet above the ground with an initial velocity of 1000 feet per second and at an angle of above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.
A) 15,627.500 feet
B) 8,137.843 feet
C) 31,252.187 feet
D) 31,254.999 feet
E) 16,268.138 feet
above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.A) 15,627.500 feet
B) 8,137.843 feet
C) 31,252.187 feet
D) 31,254.999 feet
E) 16,268.138 feet
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