A small object is sliding down at constant speed v from an inclined plane tilted at angle 0 to horizontal surface. What is the instantaneous rate of change of the distance between the object and point A?
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- An object travels in a vertical circle of 1.43 m radius. When the object is traveling downward and is 28.0° from its lowest point, its total acceleration is a = (18.51 + 16.2ĵ) m/s². At this instant, determine the following. (Take the angle 28.0° clockwise from the axis of the circle that intersects the center and the lowest point. Assume that the +x axis is to the right and the +y axis is up along the page.) esc 7 (a) magnitude of the radial acceleration m/s² (b) magnitude of the tangential acceleration m/s² (c) speed of the object m/s (d) velocity of the object (Express your answer in vector form.) m/s v= 1 ² F1 Q A 1 N 2 Q F2 W S 3 X # H option command 80 F3 E D $ 4 C 990 GOD F4 R F % 67 8 5 F5 V T MacBook Air 6 G F6 Y B & 7 H 4 F7 U N 00 * 8 J FB 1 ( 9 M F9 K O O < A I -10 L || ! P V F11 1 + { [ 2 412 1 - option commandA cork bobs up and down in a lake. The distance from the bottom of the lake to the center of the cork at time t>=0 is given by s(t)= 25+cos(pi t), where s(t) is in feet and t Is in seconds. During what time interval is the cork rising. Draw pictures as wellA particle starts from the origin at r=0 with a velocity of 8.0 m/s and moves in the xy plane with constant acceleration (3.5i +1.7)) m/s1. (a) When the particle's x coordinate is 27 m, what is its y coordinate? (b) When the particle's x coordinate is 27 r. what is its speed? m/s
- A student standing on a cliff that is a vertical height d = 8.0 m above the level ground throws a stone with velocity v0 = 23 m/s at an angle θ = 16 ° below horizontal. The stone moves without air resistance; use a Cartesian coordinate system with the origin at the stone's initial position. A) With what speed, vf in meters per second, does the stone strike the ground? B) If the stone had been thrown from the clifftop with the same initial speed and the same angle, but above the horizontal, would its impact velocity be different? If the stone had been thrown from the clifftop with the same initial speed and the same angle, but above the horizontal, would its impact velocity be different?b) I(1, 0, 0), J(0, 1, 0), and K(0, 0, 1) 6, A helicopter takes off at a ground velocity of 150 km/h. It climbs at an angle of 48° toward the east. A 17-km/h wind is blowing from the south. Determine the resultant air and ground velocities. Include a diagram in your solution. The Eiffel Tower is 324 m tall. Denise isAn object slides along the inside of a vertical circular track and never loses contact with the track. As it slides upward it slows down, and as it slides downward it speeds up. It's not known whether it's moving clockwise or counterclockwise in the view shown. Match points A, B, C, and D with possible acceleration vectors at those points. Only one of the acceleration vectors shown is possible at each point. A с a B
- A woman rides a carnival Ferris wheel at radius 18 m, completing 4.8 turns about its horizontal axis every minute. What are (a) the period of the motion, and the magnitude of her centripetal acceleration at (b) the highest point and (c) the lowest point? (a) Number i Units (b) Number i Units (c) Number i UnitsA woman stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v0 = 21.5 m/s. The stone leaves her hand at a height of h = 57.0 m above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the stone leaves the hand. Write the equations for the position of the stone with time, using the coordinates in the figure. Use the following as necessary: t. Assume that x and y are in meters and t is in seconds.A bicyclist is at the bottom of a hill with a speed of 30 ft/s. After traveling 600 ft on the road, she reaches the top of the hill with a speed of 15 ft/s. Her total acceleration at the top of the hill is 1.3 ft/s^2. Assuming her acceleration along the road is constant. -What is the radius of curvature for the top of the hill?
- A woman stands at the edge of a cliff and throws a pebble horizontally over the edge with a speed of v0 = 20.5 m/s.The pebble leaves her hand at a height of h = 55.0 m above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the pebble leaves the hand. Answer parts a-f.You are on a train that is traveling at 3.0 m/s along a level straight track. Very near and parallel to the track is a wall that slopes upward at a 12° angle with the horizontal. As you face the window (0.777 m high, 2.26 m wide) in your compartment, the train is moving to the left, as the drawing indicates. The top edge of the wall first appears at window corner A and eventually disappears at window corner B. How much time, in seconds, passes between appearance and disappearance of the upper edge of the wall? A B A 3.0 m/s 12⁰ BA firework is launched with an initial velocity of 30 m/s at an angle of 65 degrees with respect to the horizontal. The peak height of the firework, just before it explodes. b. The vertical component of the firework’s velocity, just as it reaches the peak of its motion and explodes. c. The horizontal distance traveled by the firework, just as it reaches the peak of its motion and explodes.