Question

A charged particle is projected in the air such that its horizontal (x) and vertical (y) shifts are given by x(t) = 10t − t2 and y(t) = 6t, where x and y are in meters and time t is in seconds. What is the ratio of y to x at t = 4 seconds?

Answer 1

`\bf \stackrel{ratio}{y:x}\implies \cfrac{y}{x}\implies \left. \cfrac{6t}{10t-t^2} \right|_(t=4)\implies \cfrac{6(4)}{10(4)-(4)^2} \\\\\\ \cfrac{24}{24}\implies \cfrac{1}{1}\implies \stackrel{ratio}{1:1}`