Exam 4: Two- and Three-Dimensional Motion

While the gondola is rising at a speed of 2.0 m/s, a passenger in a balloon-supported gondola throws a small ball down at a speed of 5.0 m/s relative to his body. A person who measures the ball's velocity at the instant of release will find that the ball's velocity relative to the ground at that instant is

The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by ​ . ​ The magnitude, in meters, of the plane's displacement from the origin is

A rifle is aimed horizontally at the center of a large target 60 m away. The initial speed of the bullet is 240 m/s. What is the distance from the center of the target to the point where the bullet strikes the target?

A tennis player standing 12.6 m from the net hits the ball at 3.00° above the horizontal. To clear the net, the ball must rise at least 0.330 m. If the ball just clears the net at the apex of its trajectory, how fast was the ball moving when it left the racket?

A rock is projected from the edge of the top of a building with an initial velocity of 12.2 m/s at an angle of 53° above the horizontal. The rock strikes the ground a horizontal distance of 25 m from the base of the building. Assume that the ground is level and that the side of the building is vertical. How tall is the building?

A student in the front of a school bus tosses a ball to another student in the back of the bus while the bus is moving forward at constant velocity. The speed of the ball as seen by a stationary observer in the street

A tennis player wants to slam a serve at O so that the ball lands just inside the opposite corner of the court. What should the ratio be for the initial velocity ? The time t = 0 is the time when the ball is hit by the racket. ​ ​

Newton approximated motion in a circle as a series of linear motions, as in the polygon below. Assume that the particle moves at constant speed vA from A to B, and at constant speed vB from B to C. Use this exhibit to answer the following question(s). -The direction of the acceleration, , at point B, is shown by the arrow in

Two cooks standing side by side in a restaurant pull their beaters out of the dough at the same instant. A glob of dough flies off each beater. Each glob lands on the top of a tin the same horizontal distance away and at its initial height. However, one lands later than the other. The explanation is that they left the beaters at angles θ₁ and θ₂ such that:

Two balls, projected at different times so they don't collide, have trajectories A and B, as shown below. Which statement is correct?

A fast duck is flying mi/h at the same altitude as a slow airplane flying with a velocity of mi/h. How fast and in what direction is the duck moving relative to the airplane?

A car is driven 1200 m north at 20.0 m/s and then driven 1600 m east at 25.0 m/s. What are the magnitude and direction of the displacement for this trip?

Newton approximated motion in a circle as a series of linear motions, as in the polygon below. Assume that the particle moves at constant speed vA from A to B, and at constant speed vB from B to C. Use this exhibit to answer the following question(s). - The direction of the change in velocity, , at point B, is shown by the arrow in

Given the equations below, which description best fits the physical situation? ​ ​

A particle starts from the origin at t = 0 with a velocity of 6.0 m/s and moves in the xy plane with a constant acceleration of m/s². At the instant the particle achieves its maximum positive x coordinate, how far is it from the origin?

A particle moves in the xy plane in a circle centered on the origin. At a certain instant the velocity and acceleration of the particle are m/s and m/s². What are the x and y coordinates of the particle at this moment?

Jane plans to fly from Binghampton, New York, to Springfield, Massachusetts, about 280 km due east of Binghampton. She heads due east at 280 km/h for one hour but finds herself at Keene, which is 294 km from Binghampton in a direction 17.8 degrees north of due east. What was the wind velocity?

While her kid brother is on a wooden horse at the edge of a merry-go-round, Sheila rides her bicycle parallel to its edge. The wooden horses have a tangential speed of 6 m/s. Sheila rides at 4 m/s. The radius of the merry-go-round is 8 m. Use this exhibit to answer the following question(s). - At what time intervals does Sheila encounter her brother, if she rides in the direction of rotation of the merry-go-round?

A car travels in a due northerly direction at a speed of 55 km/h. The traces of rain on the side windows of the car make an angle of 60 degrees with respect to the horizontal. If the rain is falling vertically with respect to the Earth, what is the speed of the rain with respect to the Earth?

A carnival Ferris wheel has a 15-m radius and completes five turns about its horizontal axis every minute. What is the acceleration of a passenger at his lowest point during the ride?