The speed of the ball is ds/dt = 32t At t =1/2 s ds/dt = 16 ft/s The distance from the ground 50 - 16(1/2)^2 = 46 ft The triangles formed are similar 50/46 = (30 + x)/x x = 345 ft
50 / (50 - s) = (30 + x)/x Taking the derivative and substituing ds/dt = 16 and Solve for dx/dt
We have to find the lengths of the diagonals KM and JL: d ( KM ) = √ (( - a - b )² + ( 0 - c )²) = √ (( a + b )² + c² ) d ( JL ) = √ ( ( a - ( - b ) )² + ( 0 - c )²) = √ ( ( a + b )² + c² ) So the lengths of the diagonals KM and JL are congruent. The lengths of the diagonals of the isosceles trapezoid are congruent.