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Question Number 188203 by moh777 last updated on 26/Feb/23

Answered by mr W last updated on 26/Feb/23

$$g=32.2ft/s^2$$$$\left(1\right)$$$$h_1=v_1(t+3)-\frac{g{(t+3)}^2}{2}$$$$h_2=v_{2}t-\frac{{gt}^2}{2}$$$$h_1=h_2=350ft$$$$v_1(t+3)-\frac{g{(t+3)}^2}{2}=h_1=350$$$$t+3=\frac{1}{g}(v_1\pm \sqrt{v_1^2-2{gh}_1})$$$$=\frac{160\pm \sqrt{{160}^2-2\times 32.2\times 350}}{32.2}$$$$=6.687sor3.251s$$$$t=3.687sor0.251s$$$$v_{2}t-\frac{{gt}^2}{2}=h_2=350$$$$\Rightarrow v_2=\frac{350+\frac{32.2\times 3.{687}^2}{2}}{3.687}=154.289ft/s$$$$or$$$$\Rightarrow v_2=\frac{350+\frac{32.2\times 0.{251}^2}{2}}{0.251}=1398.463ft/s$$$$thatmeanstherearetwopossibilities.$$$$possibility1:ball2withinitial$$$$velocity1398.463ft/sor$$$$possibility2:ball2withinitial$$$$velocity154.289ft/s.$$$$\left(2\right)$$$$inpossibility1theball1isascending$$$$andinpossibility2theball1is$$$$descending.$$$$\left(3\right)$$$$ball1:$$$$v_{1}t-\frac{{gt}^2}{2}=0$$$$t=\frac{2v_1}{g}=\frac{2\times 160}{32.2}=9.938s$$$$ball2:$$$$t=\frac{2v_2}{g}=\frac{2\times 1398.463}{32.2}=86.861s\left(possibilty1\right)$$$$t=\frac{2v_2}{g}=\frac{2\times 154.289}{32.2}=9.583s\left(possibilty1\right)$$

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