Answer to Question #228648 in Algebra for Nomo

Question

7, A ball A is thrown upward at the same time with a ball B. The initial speed of A is half that of B. What is the distance of A from the top of B?

Answer 1

$\text{We know that $v^2 =u^2+2gh$, at maximum height velocity is 0, therefore we have}\\ U_A^2 = -2gh_A-(1)\\ U_B^2 = -2gh_B\\ \text{But $U_A=\frac{U_B}{2}$}\\ \implies 4U_A^2 = -2gh_B\\ h_B= -\frac{4U_A^2}{2g}\\ \text{From (1), we have that $h_A=-\frac{U_A^2}{2g}$}\\ \therefore h_B = 4h_A\\ \text{Hence, the difference between the distance of A and B is 4A-A= 3A }$