Draw the workspace of the following planar manipulator: 2.5 0.5 5 e, For 0 < 0, < 135° +180° < 02 < +45° 0 < 0z < 360°

In the figure here, a small, solid, uniform ball is to be shot from point P so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance d from the right edge of the plateau. The vertical heights are h, = 3.5 cm and h2 = 1.70 cm. With what speed must the ball be shot at point P for it to land at d = 4.5 cm? Ball

You are working with a movie director and investigating a scene with a cowboy sliding off a tree limb and falling onto the saddle of a moving horse. The distance of the fall is several meters, and the calculation shows a high probability of injury to the cowboy from the stunt. Let's look at a simpler situation. Suppose the director asks you to have the cowboy step off a platform 2.55 m off the ground and land on his feet on the ground. The cowboy keeps his legs straight as he falls, but then bends at the knees as soon as he touches the ground. This allows the center of mass of his body to move through a distance of 0.670 m before his body comes to rest. (Center of mass will be formally defined in Linear Momentum and Collisions.) You assume this motion to be under constant acceleration of the center of mass of his body. To assess the degree of danger to the cowboy in this stunt, you wish to calculate the average force upward on his body from the ground, as a multiple of the cowboy's…

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