Find an expression of the ball's speed in terms of a, h, y, and g. Express your answer in terms of some or all of the variables a, h, y, and the free-fall acceleration g. n
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- A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 254 m, and the car completes the turn in 32.0 s. y An xy cordinate system is shown. Three points A, B, and Carhown on the graph These points arepined by a dotted curve. Poin v-axis, pont while p O is on te negative the posive x-axis, 35.0° Corant I X-axis. at an ang From poir right upward to cross B and en meets C. An arrow indcating theelocity at point A points hA to the right. An arrow indicating the velocity at point C points vertically upward. A the lly moves long B curves (a) What is the acceleration when the car is B located at an angle of 35.0°? Express your answer in terms of the unit vectors î and j. |-0.196 First find the magnitude of the acceleration; then work out the components of the vector. m/s2 î +|-0.137 Note that 254 is one quarter of the circumference of the circular path. m/s2 j (b) Determine the car's average speed.…A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 263 m, and the car completes the turn in 33.0 s. 35.0° В A (a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors î and ĵ. m/s? î + m/s? j (b) Determine the car's average speed. m/s (c) Determine its average acceleration during the 33.0-s interval. m/s? ĵ m/s2 î +A motorcycle moves on a circular path of radius b. The motorcycle starts from rest and its speed increases at a constant rate c. Use polar coordinates to find the angle between its velocity and acceleration vectors. Is the angle constant?
- Airplane makes a gradual 90 degrees turn while flying at a constant speed of 200 m/s. The process takes 20.0 seconds to complete. 1. for this turn, the magnitude of the radial acceleration of the plane is?A runner runs around a circular track. He completes one lap at a time if t=497s at a constant speed of v=3.9m/s. What is the radius r in meters of the track?what was the runners centripetal acceleration ac in m/s^2 during the run?A ball is traveling at a constant speed (v) of 40.0 m/s in a circle with a radius (r) of 6.0 m. (Hint: The circumference C = 2πr) The centripetal acceleration is ZERO a. False b. True The total distance traveled by the ball is: How long in time does it take for the ball complete one circle? The displacement traveled by the ball is: The average speed of the ball is: The average velocity of the ball is:
- A car driving around a circular track has a centripetal acceleration of 91 m/s291 m/s2 until it hits a slick spot and slides straight off the track. If the radius of the track is 67 m,67 m, what is the car's speed ?v when it leaves the track?A skier/snowboarder starts at rest at the top of a snowy (friction-free) hill with height h1. After the bottom of this hill there is a small “jump” hill. The top of the jump has height h2 and a curvature of radius R. What is the minimum height of the starting hill, h1min, so that the skier/snowboarder jumps or “catches air” at the top of hill 2? Solve for h1min in terms of h2, R, and g. Hint: if the skier/snowboarder jumps, he/she/they lose contact with the snowy ground.7.A Jogger runs along a circular track of radius R = 100.0 m. She starts at A and jogs three-fourths of the circular track, un to B She then turns back and jogs one-half of the circular track, up to C. (Note that the dashed line is only a guide for the eye - showing that B, the center of the circle, and C are collinear). A. What is the distance she traveled? B. Draw her displacement vector. C. What is the magnitude of her displacement? C R. A 3. B 66
- In 1780, in what is now referred to as “Brady’s Leap,” Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running horizontally off the edge of the cliff above Ohio’s Cuyahoga River, which is confined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt 22 ft across while falling 20 ft. Tall tale, or possible?a. What is the minimum speed with which he’d need to run off the edge of the cliff to make it safely to the far side of the river?b. The world-record time for the 100 m dash is approximately 10 s. Given this, is it reasonable to expect Brady to be able to run fast enough to achieve Brady’s leap?Algebraic relation. A toy rocket leaves the horizontal ground and reaches a maximum height of h. The rocket then returns back to the ground a distance d Bh from the launch point. If 3 = 2.17, determine the launch angle with respect to the horizontal. Notice that you should not calculate the launch angle in degrees. Instead, you should supply the correct numerical argument for the inverse tangent function. 1 0 = tan ¹ ( Record your numerical answer below, assuming three significant figures.An object moves in a horizontal circle at constant speed v (in units of m/s). It takes the object T seconds to complete one revolution. a. Derive an expression that gives the radial acceleration of the ball in terms of v and T, but not r. b. If the speed doubles, by what factor must the period T change if arad is to remain unchanged?