Chapter 3 Two-Dimensional Motion and Vectors

Question In terms of A and B, what vector operation does R represent? A B R A -B

Answer R = A – B

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)?

Answer 54.7 m east

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)

Answer Y component = 63.5 m X component = m

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)

Answer R = ⁰ East of South (or 45⁰ south of east)

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)

Answer ⁰ north or west (or 87.7⁰ west of north)

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)

Answer 0.23 s

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)

Answer 1.11 m

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)

Answer 4.24 m

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?

Answer m

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?

Answer No he doesn’t make it, he only jumps a distance of 1.2 m.

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)

Answer ⁰ east of north (or 63.23⁰ north of east)

Question A passenger at an airport steps onto a moving sidewalk that is 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?

Answer 2.5 m/s in the direction of the moving sidewalk

Question True or False: It is possible for a vector to have a component that is greater than its magnitude.

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.

Question Under what circumstance would a vector have components that are equal in magnitude?

Answer When the vector is oriented at a 45⁰ angle

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?

Answer They both hit at the same time

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?

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.

Question For a projectile fired at an angle, at what point in its path does it have minimum speed?

Answer At the top of its path

Question For all projectiles, how does the horizontal component of velocity change as the object follows a parabolic path?

Answer Horizontal speed does not change; remains constant

Question Vertically, what type of one-dimensional motion does a projectile mimic?

Answer Free fall

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?

Answer 15⁰

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)

Answer ⁰ south of east/below the horizontal (or 37.4⁰ east of south/to the right of the vertical)

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)

Answer 99.7 m/s