Question

Which represents t in terms of v?

Answer 1

`\large\boxed{(-v\pm√(v^2-19.6h))/(-9.8)}`

Explanation:

`h=-4.9t^2+vt\\h>0\ and\ v>0\\\\-4.9t^2+vt=h\qquad\text{subtract}\ h\text{from both sides}\\\\-4.9t^2+vt-h=0`

`\text{The quadratic formula:}\\\\ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta<0,\ then\ NO\ SOLUTION\\if\ \Delta=0,\ then\ ONE\ SOLUTION\\if\ \Delta>0,\ then\ TWO\ SOLUTIONS\ x=(-b\pm\sqrt\Delta)/(2a)`

`-4.9t^2+vt-h=0\\\\a=-4.9,\ b=v,\ c=-h\\\\\Delta=v^2-4(-4.9)(-h)=v^2-19.6h\\\\t=(-v\pm√(v^2-19.6h))/(2(-4.9))=(-v\pm√(v^2-19.6h))/(-9.8)`