Aprojectile is launched from ground level with an initial speed of 48.7 m/s. find the launch angle (the angle the initial velocity vector is above the horizontal) such that the maximum height of the projectile is equal to its horizontal range. (ignore any effects due to air resistance.)

When a vertical beam of light passes through a transparent medium, the rate at which its intensity i decreases is proportional to i(t), where t represents the thickness of the medium (in feet). in clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity i0 of the incident beam. what is the intensity of the beam "10" feet below the surface? (give your answer in terms of i0. round any constants or coefficients to five decimal places.)

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.

Friction removes energy from objects in motion. which statement best describes how this works? a) friction transforms ke into thermal energy b) friction transfers thermal energy to ke c) friction transforms te into pe d) friction transforms pe into ke e) friction transfers ke into pe