2024 F=ma

#1An archer fires an arrow from the ground so that it passes through two hoops, which are both a height h above the ground. The arrow passes through the first hoop one second after the arrow is launched, and through the second hoop another second later. What is the value of h?

#2An amusement park ride consists of a circular, horizontal room. A rider leans against its frictionless outer walls, which are angled back at 30° with respect to the vertical, so that the rider's center of mass is 5.0 m from the center of the room. When the room begins to spin about its center, at what angular velocity will the rider's feet first lift off the floor?

#3A ball is dropped from a height of 5 m (ignore air resistance). With g = 10 m/s², what is its speed just before hitting the ground?

#3A simple bridge is made of five thin rods rigidly connected at four vertices (see figure). The ground is frictionless, so that it can only exert vertical normal forces at B and D. The weight of the bridge is negligible, but a person stands at its middle, exerting a downward force F at vertex C. In static equilibrium, each rod can be experiencing either tension or compression. Which of the following is true?

#7A 1 kg ball moving at 4 m/s collides with and sticks to a stationary 3 kg ball. What is their common velocity afterward?

#12A car rounds a flat curve of radius 50 m. The coefficient of friction between tires and road is 0.4, g = 10 m/s². What is the maximum speed without skidding?