Question

A small, spring-loaded cannon launches a racquetball from level ground with an initial speed v, at an angle 0, with the horizontal. The racquetball lands a horizontal distance R from its launch point. The highest point the racquetball reaches during its flight is a distance above the ground. In terms of R and g, find the following. (You may ignore air resistance.) 12 (a) the time interval during which the racquetball is in motiorn (b) the racquetball's speed at the peak of its path (c) the initial vertical component of its velocity yi

Answer 1

For same level projectile, H-Max = v_i^2 (sin theta_i)^2/2g and Range = V_i^2 sin(2 theta_i)/g H_max = R/12 = (v_i sin theta_i)^2/2g implies v_i sin theta_i = squareroot Rg/6 t = 2V_i Sin theta_i/g = 2/g squareroot Rg/6 t = squareroot 2R/3g b) Range/time = V_i^2(2 sin theta cos theta)/2V_i sin theta_i = V_i cos theta v_i cos theta = (R)/squareroot 2R/3g = squareroot 3gR/2 V = squareroot 3g R/2 c)v_yi = V_i sin theta_i = squareroot R_g/6 V_y_i = squareroot R_g/6