An 800kg roller coaster traveling at 10m/s is 80m above the bottom of the track. a. How fast is the roller coaster car traveling at the bottom of the hill? b. How fast is the roller coaster car traveling at the top of the loop?
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- An 800kg roller coaster traveling at 10m/s is 80m above the bottom of the track. a. How fast is the roller coaster car traveling at the bottom of the hill? b. How fast is the roller coaster car traveling at the top of the loop?
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- A frictionless rolling cart has an initial velocity of 10.0 m/s as it climbs up anincline of 24 degrees .a. What is the cart’s height above the ground when it monetarily comes to astop on the ramp?b. At that instant, how far has it travelled along the ramp?An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers. If the plane is traveling east at 40 m/s and is 100 meters above the ground: a.Using the release point as the origin, find the time it takes for the package to reach the ground once released. b.How far east of the release point does the package strike the ground? Also, What is the speed of the package as it hits the ground? c.With what angle (below the horizontal) does the pack strike the ground? Please show work for all of the parts.. A stone is thrown from level zero at 30° above horizontal. It lands at the same level 20 m away.a. What is the initial speed of the stone?b. What is the maximum height that it reaches during the flight?c. How long does the whole flight take?
- Suppose that the gravitational acceleration on a certain planet is only 3.0 m/s2. A space explorer standing on this planet throws a ball straight upward with an initial velocity of 18 m/s. a. What is the velocity of the ball 4 seconds after it is thrown? b. How much time elapses before the ball reaches the highpoint in its flight?A helicopter blade spins at exactly 110 revolutions per minute. Its tip is 9.5 m from the center of rotation. A. What is the average speed of the blade tip in the helicopter's frame of reference, in meters per second? B. What is the average velocity over one revolution, in meters per second?m L 4. A box with a mass m = 0.4 kg is released from rest at the top of a curved section of a track that is one quarter of a circle with a radius R = 0.2m. When the box reaches the bottom of the curved track it slides on a horizontal section of the track. There is no friction on the curved section of the track. a. Find the velocity of the box at the bottom of the curved section of the track. b. Find the normal force on the block when it is at the bottom of the circular section of the ramp. If there is a Resistive force F on the horizontal section of the track and is given as a function of speed by F=-4v² c. Write down the differential equation for the speed of the block. 1 d. Show that the solution can be written as: v = 0.5 + 10t
- David is buying a jet boat this summer and spending a lot of time zooming around. One place he plans on going is to the Plate River above Albany, NY. The current is 4 m/s south and the river is 200m wide. the boat will move at 20 m/s at full throttle, his only setting. A. how quickly will he cross the river if he heads straight across?B. how far downstream will he end up if he does so?C. if he wants to go straight across, what angle upstream should he use?4. A ball is shot from a cannon at 50 m/s at an angle of 30° above the horizontal. a. Draw a labeled diagram with all relevant information. Note directions you chose to be +x and +y. b. How far has the ball traveled horizontally when it reaches its highest point in the flight? How high is it at this point? c. What is the speed of the ball at the highest point in its flight?A ball is thrown horizontally from a cliff of height 90 meters with an initial speed of 45 m/s. A. How far from the base of the cliff will it strike the ground? B. What is its vertical component of velocity when it strikes the ground? C. What is its speed when it strikes the ground?
- Prior to landing at the airport, an airplane flies at a constant speed in a circular course with aradius of 5000 meters. An observer notices that the plane completes each round trip in 400seconds.a. What is the speed of the airplane? b.Whats the centripetal acceleration?On the Apollo 14 mission to the moon, astronaut Buzz Aldrin hit a golf ball with a golf club improvised from a tool. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hit the ball with a speed of 29 m/sm/s at an angle 22 ∘∘ above the horizontal. a. how long was the ball in flight in seconds? b. how far did it travel in meters? c. If there was no air resistance, how much farther would it travel in meters on the moon than on earth?H6. 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 loose contact with the snowy ground.