PHYS 1401 College Physics I CRN 55178 HOMEWORK PROBLEMS Khalid Bukhari HW 3 Chapter 3 VECTORS AND TWO DIMENSIONAL MOTION PART A Hand in your answers in class on scantron on Wednesday 15 September 2010 1 A catapult launches a large stone at a speed of 45 0 m s at an angle of 55 0 with the horizontal What maximum height does the stone reach Neglect air friction a 45 7 m b 32 7 m c 69 3 m d 83 2 m e 102 m At maximum height y hmax the vertical velocity of the stone will be zero Thus v2y v02 y 2 a y Dy gives hmax 2 45 m s sin 2 55 0 0 v02 sin 2 q 69 3 m 2 g 2 9 80 m s2 v2y v02 y 2a y and we see that choice c is the correct answer 2 A skier leaves the end of a horizontal ski jump at 22 0 m s and falls 3 20 m before landing Neglecting friction how far horizontally does the skier travel in the air before landing a 9 8 m b 12 2 m c 14 3 m d 17 8 m e 21 6 m The skier has zero initial velocity in the vertical direction 0y 0 and undergoes a vertical displacement of Dy 3 20 m The constant acceleration in the vertical direction is a y g so 1 2 we use Dy v0 y t 2 a y t to find the time of flight as 3 20 m 0 2 3 20 m 1 9 80 m s 2 t 2 or t 9 80 m s2 0 808 s 2 During this time the object moves with constant horizontal velocity v x v0 x 22 0 m s The horizontal distance traveled during the flight is Dx v x t 22 0 m s 0 808 s 17 8 m which is choice d 3 A cruise ship sails due north at 4 50 m s while a coast guard patrol boat heads 45 0 north of west at 5 20 m s What is the velocity of the cruise ship relative to the patrol boat a vx 3 68 m s vy 0 823 m s b vx 3 68 m s vy 8 18 m s c vx 3 68 m s vy 8 18 m s d vx 3 68 m s vy 0 823 m s e vx 3 68 m s vy 1 82 m s Choose coordinate system with north as the positive y direction and east as the positive r x direction The velocity of the cruise ship relative to Earth is v CE 4 50 m s due north with r r components of vCE x 0 and vCE y 4 50 m s The velocity of the patrol boat relative to r Earth is v PE 5 20 m s at 45 0 north of west with components of vr PE x vr PE cos 45 0 5 20 m s 0 707 3 68 m s 1 PHYS 1401 College Physics I and CRN 55178 Khalid Bukhari HW 3 r v PE sin 45 0 5 20 m s 0 707 3 68 m s r r r Thus the velocity of the cruise ship relative to the patrol boat is vCP v CE v PE which has components of vr CP x vr CE x vr PE x 0 3 68 m s 3 68 m s and vr PE y vr CP y r r v CE y v PE y 4 50 m s 3 68 m s 0 823 m s Choice a is then the correct answer 4 An athlete runs three fourths of the way around a circular track Which of the following statements is true a His average speed is greater than the magnitude of his average velocity b The magnitude of his average velocity is greater than his average speed c His average speed is equal to the magnitude of his average velocity d His average speed is the same as the magnitude of his average velocity if his instantaneous speed is constant e None of statements a through d is true 5 A car moving around a circular track with constant speed a has zero acceleration b has an acceleration component in the direction of its velocity c has an acceleration directed away from the center of its path d has an acceleration directed toward the center of its path or e has an acceleration with a direction that cannot be determined from the information given 6 A NASA astronaut hits a golf ball on the Moon Which of the following quantities if any remain constant as the ball travels through the lunar vacuum a speed b acceleration c velocity d horizontal component of velocity e vertical component of velocity 7 A baseball is thrown from the outfield toward the catcher When the ball reaches its highest point which statement is true a Its velocity and its acceleration are both zero b Its velocity is not zero but its acceleration is zero c Its velocity is perpendicular to its acceleration d Its acceleration depends on the angle at which the ball was thrown e None of statements a through d is true 8 A student throws a heavy red ball horizontally from a balcony of a tall building with an initial speed v0 At the same time a second student drops a lighter blue ball from the same balcony Neglecting air resistance which statement is true a The blue ball reaches the ground first b The balls reach the ground at the same instant 2 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 3 c The red ball reaches the ground first d Both balls hit the ground with the same speed e None of statements a through d is true 9 John throws a baseball from the outfield from shoulder height at an initial velocity of 29 4 m s at an initial angle of 30 0 with respect to the horizontal The ball is in its trajectory for a total interval of 3 00 s before the third baseman catches it at an equal shoulder height level Assume air resistance negligible What is the ball s horizontal displacement a 76 4 m b 38 2 m c 57 3 m d zero Vx 29 4 Cos 30 25 46 m s Distance Vx t 25 46 3 76 4 m 10 A stone is thrown at an angle of 30 above the horizontal from the top edge of a cliff with an initial speed of 12 m s A stop watch measures the stone s trajectory time from top of cliff to bottom to be 5 6 s How far out from the cliff s edge does the stone travel horizontally g 9 8 m s2 and air resistance is negligible a 58 m b 154 m c 120 m d 197 m Vx 12 Cos 30 10 39 m s Distance Vx t 10 39 5 6 58 2 m …