a convex lens has a focal length f. an object is placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. the image is located at what distance from the lens?

Planck decided to assume that atoms could only vibrate at certain frequencies that were whole numbers eg 2f, 3f and so on. others used to think that atoms vibrate continuously

Since you have not included the experiment situation and the data, of course, i can not give you specific details about it. but i can you with this question.1) i will assume that the motion is projectile (parabolic) motion.2) yes, the horizontal distance depends on the horizontal velocity as, naming vx the horizontal velocity and t the time, it is: x = vx × t3) now, observe that the flight time depends on the vertical velocity as, naming voy the initial vertical velocity, t the time and y the vertical distance before reaching the ground: y = yo + voy×t - gt² / 2.the higher the initial vertical velocity (voy) the longer the object will be flying and so t will be higher in the equation for the horizontal distance.that explains the relationship between the horizontal distance and the horizontal velocity.