# Useful Formulae

28 GRAVITYANDPROJECTILES featherless falling objects Newtons Law of Universal Gravitation states that any two masses m1 and m2 at a distance dapart will exert equal and opposite forces on each other of magnitude Fwhere Gis the universal gravitation constant see appendix. Note that d is the distance between the centres of massof m1 and m2. Near the surface of the Earth mass m2,d is effectively constant, giving the localgravitational accelerationconstant g. g 9.80665 msec2 so that F m1g. Assuming negligible air resistance, an object falling from rest will travel smetres intsecondswhere sand tare related by s gt2 or t The objects velocity at time twill be v gt 2gs msec. Note that these quantities are independent of mass. The path of a projectile with initial velocity vand angle of trajectory is given by xt vtcos and yt vtsin gt2 These are timedependent coordinates. Gm2 d2 2s g Gm1m2 d2 F 29