a projectile is shot from the edge of a cliff 125 mabove ground level with an in

Question

a projectile is shot from the edge of a cliff 125 mabove ground level with an inital speed of 65.0 m/s at an agnle of37 degrees with the horizontal, as shown in fig 3-35. (a) determine the time taken by the projectile to hit point Pat ground level (b) determine the range X of the projectile as measured fromthe base of the cliff. at the instant just before theprojectile hits pont P, find (c)the horizontal and the verticalcomponents of its velocity (d)the magnitude of the velocity and (e) the angle made by the velocity vector with thehorizontal

Explanation / Answer

velocity v = 65 m / s angle = 37 degrees height h = 125 m the time taken by the projectile to hit point P at groundlevel T = t+ t' where t = time taken to reach maximum height = v sin / g = 3.991 s maximum height from the top of cliff h ' = ( v sin ) 2 / 2g                                                            = 78 m maximum height from ground H = h+ h ' = 203 m t ' = time taken to travel from H height to ground = [2H / g ]      = 6.437 s So, required time T = t+ t ' = 10.42 s (b). Horizontal range X = ( v cos ) * T                                     = 541.36 m (c).Horizontal component of velocity u = v cos = 51.91 m / s vertical component of velocity u ' = gT                                              = 102.116 m / s (d).magnitude of velocity = [ u ^ 2+ u '^2]                                        =114.55 m / s (e). required angle = tan -1 ( u ' / u )                               = 63 degrees

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