In an experiment, you hold a stationary block of mass m = 4.50 kg at the top of a 2.3 m long frictionless incline. You release the block and measure its speed at the bottom of the ramp to be 4.1 m/s. Determine the angle between the horizontal and the surface of the incline.

During a rescue mission, three firefighters are linked together by a rope as they ascend a steep slope. The slope is inclined at 35° to the horizontal, as shown in the diagram. Unexpectedly, the last firefighter loses footing, leading the second firefighter to also lose balance. Fortunately, the first firefighter successfully supports both of them. With each firefighter weighing 70 kg, determine the tension in each of the two segments of the rope connecting the three firefighters. Assume negligible friction between the slipping firefighters and the surface.

A book was tossed up with an initial speed of 6.5 m/s on an inclined plane. The inclined plane makes an angle of 32° with the horizontal axis shown in the figure below. Ignoring friction, calculate the time it takes for the book to return to its initial position.

In a shipping facility, workers use a manual loading ramp to move heavy crates into freight trucks. To optimize efficiency while ensuring that workers do not exert more than 100 N of force pushing the crates upward, what is the maximum angle at which the loading ramp can be set? Assume the average crate has a mass of 40 kg, and ignore the effects of friction.

Two masses m_p = 7.80 kg and m_q = 10.6 kg are connected as shown in the figure below. Determine the tension in the rope connecting them.

A coupe starts from rest and descends a 1-in-5 slope (where for every 5m of horizontal distance, the elevation varies by 1m). If friction is ignored, determine its speed at the bottom of the slope, after covering a distance of 60m.