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Published byRodger Wells Modified over 8 years ago
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Chapter 3 Two-Dimensional Motion and Vectors
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Question In terms of A and B, what vector operation does R represent? A B R A -B
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Answer R = A – B
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Question One of the holes on a golf course lies 100 m due east of the tee. A novice golfer flubs his tee shot so that the ball lands only 64 m directly northeast of the tee. How far east does he still have to go to sink the ball (round to one decimal place)?
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Answer 54.7 m east
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Question Another golfer on the same hole slices the ball 30⁰ south of east so that the ball lands in a sand trap 127 m away. Find the x and y components of this vector. (round to 1 decimal place) (2 points total)
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Answer Y component = 63.5 m X component = 110.0 m
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Question On his way to class, John walks 43 m east then 52 m south then 7 m west and finally 16 m north. What is John’s displacement? Don’t forget direction and orientation! (round to 1 decimal place)
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Answer R = 50.9 m @ 45⁰ East of South (or 45⁰ south of east)
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Question A plane is flying due west at a speed of 140 m/s. The wind is blowing at a speed of 15 m/s 25⁰ west of north. What is the resultant speed of the airplane? Don’t forget direction and orientation! (round to 1 decimal point)
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Answer 153.7 m/s @ 2.3⁰ north or west (or 87.7⁰ west of north)
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Question A boy and girl are having a snowball fight. The girl uses a slingshot and fires the snowball at the boy at an angle of 40⁰ with respect to the horizontal at a speed of 3.5 m/s. How long will it take the snowball to reach its maximum height? (round to 2 decimal places)
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Answer 0.23 s
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Question The boy throws a snowball back at the girl with an initial speed of 6.1 m/s at an angle of 50⁰ with respect to the horizontal. How high does the snowball rise? (round to 2 decimal places)
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Answer 1.11 m
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Question In many locations, old abandoned stone quarries have become filled with water once excavating has been completed. While standing on a 10.0 m high quarry wall, Clarence tosses a piece of granite into the water below. If Clarence throws the rock horizontally with a velocity of 3.0 m/s, how far out from the edge of the cliff will it hit the water? (round to 2 decimal places)
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Answer 4.24 m
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Question Superman is said to be able to “leap tall buildings in a single bound.” How high a building could Superman jump over if he were to leave the ground with a speed of 60.0 m/s at an angle of 75.0⁰ to the horizontal?
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Answer 168.2 m
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Question Len is running to school and leaping over puddles as he goes. From the edge of a 1.5 m long puddle, Len jumps 0.20 m high off the ground with a horizontal velocity component of 3.0 m/s in an attempt to clear it. Determine whether or not Len sits in school all day with wet socks on. How far does Len jump?
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Answer No he doesn’t make it, he only jumps a distance of 1.2 m.
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Question A boat travels due north with a speed of 1.11 m/s relative to the current and the current moves due east at a speed of 0.56 m/s relative to the land. What is the velocity of the boat relative to the land? Don’t forget direction and orientation! (round to 2 decimal places)
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Answer 1.24 m/s @ 26.77⁰ east of north (or 63.23⁰ north of east)
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Question A passenger at an airport steps onto a moving sidewalk that is 100.0 m long and is moving at a speed of 1.5 m/s. The passenger then starts walking at a speed of 1.0 m/s in the same direction as the sidewalk is moving. What is the passenger’s velocity relative to a person riding a cart alongside the sidewalk with a speed of 5.0 m/s and in the same direction in which the sidewalk is moving?
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Answer 2.5 m/s in the direction of the moving sidewalk
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Question True or False: It is possible for a vector to have a component that is greater than its magnitude.
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Answer False; the magnitude is the hypotenuse of the right triangle while the components are the legs and the hypotenuse is always the longest side of a right triangle.
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Question Under what circumstance would a vector have components that are equal in magnitude?
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Answer When the vector is oriented at a 45⁰ angle
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Question A dart is fired horizontally from a dart gun, and another dart is dropped simultaneously from the same height. If air resistance can be neglected, which dart hits the ground first?
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Answer They both hit at the same time
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Question A rock is dropped at the same instant that a ball at the same elevation is thrown horizontally. Which will have the greater speed when it reaches ground level?
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Answer The one thrown horizontally because it will have both a vertical and horizontal component to its speed whereas the one dropped will only have a vertical component.
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Question For a projectile fired at an angle, at what point in its path does it have minimum speed?
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Answer At the top of its path
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Question For all projectiles, how does the horizontal component of velocity change as the object follows a parabolic path?
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Answer Horizontal speed does not change; remains constant
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Question Vertically, what type of one-dimensional motion does a projectile mimic?
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Answer Free fall
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Question Brandon launches a projectile at an angle of 75⁰ above the horizontal, which strikes the ground a certain distance down range. For what other angle of launch at the same speed would the projectile land just as far away?
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Answer 15⁰
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Question Harry accidentally falls out of a helicopter that is traveling at 15 m/s east. He plunges into a swimming pool 2 seconds later. Assuming no air resistance, with what speed does Harry hit the water? Don’t forget to include direction and orientation! (round to 1 decimal place)
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Answer 24.7 m/s @ 52.6⁰ south of east/below the horizontal (or 37.4⁰ east of south/to the right of the vertical)
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Question A cannonball launched with an initial velocity of 141 m/s at an angle of 45⁰ follows a parabolic path and hits a balloon at the top of its trajectory. Neglecting air resistance, how fast is it going when it hits the balloon? (round to 1 decimal place)
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Answer 99.7 m/s
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