Boat B. 10 seconds 15 m/s 20 m/s. 10 seconds 25 m/s

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1 P QUIZ #5 2 MOTION WWT08: SPEEOTS HNGING VELOITIES ELERTION Two speedboats are racing on a lake. In 0 seconds, oat goes from traveling east at 5 m/s to traveling north at 20 m/s. In interval, oat goes from 20 m/s east to 25 m/s east. oat oat 0 seconds 5 m/s 20 m/s 20 m/s 0 seconds 25 m/s student watching the race states: These two boats have acceleration for the 0-second interval since they both changed their velocities by 5 m/s in that interval. What, if anything, is wrong with this student s contention? If something is wrong, identify it, and explain how to correct it. If the contention is correct, explain why. nswer: The student s explanation is wrong since he/she took the differences in the magnitudes of the velocities rather than the actual velocity differences for the interval. The acceleration for boat will be directed at some angle to the northwest and will have a magnitude of 25m/s (the length of the v vector, since it is the hypotenuse of a right triangle) divided by 0 s, giving 2.5m/s 2. oat s acceleration is directed eastward and has a magnitude of 5 m/s divided by 0 s, giving 0.5m/s 2. v i v v f v v i v f oat oat 2-WWT09: Falling Rock and Thrown Rock Velocity Graphs Rock is dropped from the top of a cliff at instant that Rock is thrown horizontally away from the cliff. The rocks are identical. student draws the following graphs to describe part of the motion of the rocks, using a coordinate system in which the positive vertical direction is up, the positive horizontal direction is away from the cliff, and the origin is the point the rocks were released from. Rock Rock Rock Rock What, if anything, is wrong with these graphs for the motions of the two rocks? If something is wrong, identify it and explain how to correct it. If the graphs are correct, explain why. The horizontal velocity graphs need to be switched, because Rock has no horizontal velocity, and Rock has a constant horizontal velocity. The vertical graph for Rock is correct for both rock

2 Rock Rock 2-QRT0: Projectile Motion Velocity and cceleration Graphs baseball is thrown from point S in right field to home plate. The dashed line in the diagram shows the path of the ball. Use a coordinate system with up as the positive vertical direction and to the right as the positive horizontal direction, with the origin at the point the ball was thrown from (point S). Home plate S In the spaces below, sketch graphs for the indicated quantities: () The horizontal velocity vs. and the vertical velocity vs.. Explain how you d your answer. nswer: Since the positive horizontal direction is to the right, the horizontal velocity will be negative. Since up is the positive vertical direction the ball has a positive initial vertical velocity, which decreases to and then becomes negative. (2) The horizontal acceleration vs. and the vertical acceleration vs.. a (horizontal) a (vertical) Explain how you d your answer. nswer: Since there is no force in the horizontal direction there will a (horizontal) be no horizontal acceleration. The vertical acceleration is negative and equal in magnitude to g. a (vertical) 2-QRT: Projectile Motion for Two Rocks Velocity and cceleration Graphs II

3 Two identical rocks are thrown horizontally from a cliff, with Rock having a greater velocity at the instant it is released than Rock. Use a coordinate system with down as the positive vertical direction, away from the cliff as the positive horizontal direction, and with the origin at the bottom of the cliff directly below the release point. a) Sketch the velocity vs. graphs for each of the rocks. Rock (faster) Rock (slower) Rock (faster) Rock (slower) : b) Which rock hits the ground first? oth hit at. c) Which rock lands farthest from the base of the cliff? Rock, the faster rock. Explain why you drew the graphs as you did and how you d your answers. There are no forces in the horizontal direction (ignoring air resistance) so both rocks will have a constant horizontal velocity. Since Rock is slower than Rock, it will have a smaller horizontal velocity. oth rocks are thrown horizontally, so they have no initial vertical velocity. oth are acted on by gravity, so the slopes of their vertical velocity graphs are constant and equal to g, and both are positive because gravity is acting down and the positive direction is defined as down. oth rocks hit at but rock hits farther from the cliff since it travels faster in the horizontal direction. 2-QRT2: aseball Projectile Motion Velocity and cceleration Graphs baseball is thrown from point S in right field to home plate. The dashed line shows the path of the ball. Home plate S Use a coordinate system with up as the positive vertical direction and to the left as the positive horizontal direction, and with the origin at home plate. Select the graph from the choices below that best represents: ) horizontal velocity vs. graph 2) horizontal acceleration vs. graph 3) vertical velocity vs. graph 4) vertical acceleration vs. graph

4 E F G H I J K L M N O P None of these -Explain or Sketch graph nswer: There are no horizontal forces (neglecting air resistance) and the ball will have no horizontal acceleration, so the horizontal velocity will be constant. The positive direction is to the left, so the horizontal velocity will be positive. Since up is positive, the initial vertical velocity is positive, and the final vertical velocity is negative. The only vertical force is gravity acting downward, and so the acceleration is constant, negative, and equal in magnitude to g. Since the acceleration is constant, the slope of the velocity must be constant, so the vertical velocity must be a straight line sloping downward from its initial positive value to its final negative value. The answers are () ; (2) ; (3) I; and (4).

5 2-RT3: PROJETILE MOTION F TWO ROKS VELOITY GRPHS Two students throw two rocks horizontally from a cliff with different velocities. oth rocks hit the water below at but Rock hits farther from the base of the cliff. Use coordinates where up is the positive vertical direction, away from the cliff is the positive horizontal direction, and the origin is at the top of the cliff at the point of release. Sketch below velocity vs. graphs for each rock. Rock (closer) Rock (farther) +y +x Rock Rock Rock (closer) Rock (farther) Explain. nswer: There are no forces in the horizontal direction (ignoring air resistance) so both rocks will have a constant horizontal velocity. Since Rock lands farther away from the cliff than Rock, it must have had a larger horizontal velocity. oth rocks are thrown horizontally, so they have no initial vertical velocity. oth are acted on by gravity, so the slopes of their vertical velocity graphs are constant equal to g, and both slopes are negative because gravity is acting down and the positive direction is defined as up 2-RT8: rrows Maximum Heights of the arrows shown were shot from height and at angle. While the arrows have size and shape, they are made of different materials so they have different masses, and they have different speeds as they leave the bows. 0 m/s 2 m/s 6 m/s 0 m/s 90 g 80 g 00 g 80 g Rank these arrows on the maximum heights they reach. annot

6 nswer > > =. Since all of these arrows are subject to the gravitational force of the Earth, which is the same no matter what the mass of the object, the only factor determining the maximum height is the vertical component of the velocity at the given point. Since they all have angle relative to the horizontal, we can use the speed at the given point to the rankings. 2-RT9: Model Rockets Fired at an ngle Horizontal Speed at Top The six model rockets shown are all at height and have just had their engines turned off. of the rockets are aimed upward at angle, but their speeds differ. Though the rockets are all size and shape, they carry different loads so their masses vary. 25 m/s 20 m/s 20 m/s 30 m/s 800 g 600 g 800 g 400 g Rank these cases on the horizontal speed of the rockets at the top (at the maximum height). nswer > > =. Since all of these rockets are subject to the gravitational force of the Earth, which is the same no matter what the mass of the object, the only factor determining the maximum height is the vertical component of the velocity at the given point. Since they all have angle relative to the horizontal, we can use the speed at the given point to the rankings. 2-RT20: annonballs cceleration at the Top of the cannons in the figures are identical, and all are aimed at angle of 35 degrees to the horizontal. The cannonballs are all size and shape, but the masses of the cannonballs, as well as their speeds as they leave the cannons, are different. v = 80 m/s annot v = 60 m/s 6 kg 8 kg Rank these cases on the acceleration of the cannonballs when they reach their highest point. nswer:. of the cannonballs are subject to a net force due to the gravitational force of the earth which does not depend on mass, so all of the balls have acceleration throughout their motion, and this includes at the top. R2-RT2: annonballs Horizontal istance annonballs of two different masses are shot from cannons at various angles above the horizontal. The velocity of each cannonball as it leaves the cannon is given, along with the horizontal component of that velocity, which is in all cases. annot

7 v = 23. m/s 30 v = 28.3 m/s 45 v = 28.3 m/s 4 kg 45 4 kg 60 Rank these cases on the horizontal distance traveled by the cannonballs. nswer: > = >. The horizontal distance is based on x f = v o (cos t f. Thus, the range, as x f is somes called, is d by the initial speed, the angle, and the of flight. s stated in the problem and in the diagrams, the horizontal component of the velocity (v o cos is value for all six cases, 20 m/s. So, the range for this ranking task is d by the of flight, t f. The of flight is d by the y- component of the initial velocity (since for all cases the cannonballs start and end at height). Hence, the larger the y-component of the initial velocity, the longer the cannonball will be in the air and the larger its range will be. 2-RT22: annonballs Time in ir annonballs of two different masses are shot from cannons at various angles above the horizontal. The velocity of each cannonball as it leaves the cannon is given, along with the vertical component of that velocity, which is the same in all cases v = 23. m/s annot v = 28.3 m/s 30 4 kg 45 Rank these cases on the the cannonballs are in the air. nswer:. The in the air is d by the vertical component of the velocity because it will be the sum of the the ball takes to get to the top of its trajectory plus the back down to the ground. Since these cannon balls are all fired from ground and return to ground the in the air will be twice the up to the top of the trajectory. Since all of these cases have vertical component of the velocity and vertical acceleration of 9.8 m/s 2 they will all take. annot