v= 30. m/s 1. A projectile is launched horizontally at a speed of 30 meters per second from a platform above the ground. The projectile impacts the ground at a distance of 9 meters from the base of the platform. Ignore air resistance. Impact location a. Calculate the height of the platform from which the projectile was launched. b. Explain the physics concepts used to solve for the height of the platform. c. If the projectile was launched off of the platform at 50 m/s, would the time that the projectile is in the air increase, decrease, or not change? Explain your response. 2. In the diagram below, a stationary solid block of mass 0.15 kg slides down one ramp from point A and up the next ramp to point C, arriving with a velocity of 5m/s. 2.0 m 0.50m a. Write an equation that represents the motion of the block from point A to point C. Your equation should use letters & symbols from the problem, and fundamental constants, such as g. b. Determine the amount of energy that is dissipated (or "lost") due to friction between the ramp and the block. c. Explain how your solution demonstrates the application of the conservation of energy. 3. A hoop and a solid sphere are released from the top of a ramp at the same time. The objects have the same radius, but the mass of the sphere is 5M, while the hoop is M. The moment of inertia for the sphere is 2/5MR? and the hoop is MR?. a. Which object, if either, will reach the end of the ramp first? Explain your answer. b. Which object, if either, will have a greater rotational kinetic energy at the bottom of the ramp? Explain your answer. 4. A cart with a mass of 5 kg begins at rest at the top of a hill with height 0.75 meters. The cart is compressed a distance of 0.15 m against a spring with a spring constant of 200 N/m. The spring is released, causing the cart to shoot forward and then down the hill. a. Complete the qualitative energy bar chart below for the earth-cart-spring system for the time between when the cart has compressed the spring to when it has rolled down the ramp. PEG PEs KEr KER PEG PEs KET KER AENT FOR b. Explain the reasoning used to complete the energy bar chart. c. Calculate the speed of the cart at the bottom of the hill. Ignore any energy losses due to friction. Do not consider the rotational energy of the wheels in your analysis. d. If the rotational energy of the wheels were included, would the carts' speed at the bottom of the hill be greater than, less than or the same as your calculated value above? Explain your response.