Question and Answers Forum

All Questions      Topic List

Mechanics Questions

Previous in All Question      Next in All Question      

Previous in Mechanics      Next in Mechanics      

Question Number 170546 by libaolin last updated on 26/May/22

$$Solve:quadraticequationaboutt:$$$$1.\mathrm{h}={\mathrm{v}}_0\mathrm{t}+\frac{1}{2}{\mathrm{gt}}^2,2.\mathrm{x}={\mathrm{v}}_0\mathrm{t}+\frac{1}{2}{\mathrm{at}}^2$$$$\mathrm{solve}\mathrm{v}:v^2-v_0^2=2ax$$

Answered by Rasheed.Sindhi last updated on 26/May/22

$$1.\mathrm{h}={\mathrm{v}}_0\mathrm{t}+\frac{1}{2}{\mathrm{gt}}^2$$$${2\mathrm{v}}_0\mathrm{t}+{\mathrm{gt}}^2=2\mathrm{h}$$$${\mathrm{gt}}^2+{2\mathrm{v}}_0\mathrm{t}-2\mathrm{h}=0$$$$\mathrm{t}=\frac{-{2\mathrm{v}}_0\pm \sqrt{{\left({2\mathrm{v}}_0\right)}^2-4\left(\mathrm{g}\right)(-2\mathrm{h})}}{2\mathrm{g}}$$$$=\frac{-{2\mathrm{v}}_0\pm \sqrt{{4\mathrm{v}}_0^2+8\mathrm{gh}}}{2\mathrm{g}}$$$$=\frac{-{2\mathrm{v}}_0\pm 2\sqrt{{\mathrm{v}}_0^2+2\mathrm{gh}}}{2\mathrm{g}}$$$$=\frac{-{\mathrm{v}}_0\pm \sqrt{{\mathrm{v}}_0^2+2\mathrm{gh}}}{\mathrm{g}}$$$$2.\mathrm{x}={\mathrm{v}}_0\mathrm{t}+\frac{1}{2}{\mathrm{at}}^2$$$$\mathrm{Similarly},$$$$\mathrm{t}=\frac{-{\mathrm{v}}_0\pm \sqrt{{\mathrm{v}}_0^2+2\mathrm{ax}}}{\mathrm{a}}$$$$3.v^2-v_0^2=2ax$$$$v^2=v_0^2+2ax$$$$v=\pm \sqrt{v_0^2+2ax}$$$$$$

Commented by peter frank last updated on 26/May/22

$$\mathrm{thank}\mathrm{you}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com