MathDB

A projectile in flight is observed simultaneously from four radio stations which are situated at the corners of a square of side

b

. The distances of the projectile from the four stations, taken in order around the square, are found to be

R_1 , R_2 , R_3

and

R_4

. Show that

R_{1}^{2}+ R_{3}^{2}= R_{2}^{2}+ R_{4}^{2}.

Show also that the height

h

of the projectile above the ground is given by

h^{2}=- \frac{1}{2} b^2 +\frac{1}{4}(R_{1}^{2}+R_{2}^{2}+R_{3}^{2}+R_{4}^{2}) -\frac{1}{8 b^{2}}(R_{1}^{4}+R_{2}^{4}+R_{3}^{4}+R_{4}^{4}- 2 R_{1}^{2}R_{3}^{2} -2 R_{2}^{2} R_{4}^{2}).

A3