Answer:
The value of [tex]v[/tex] is ± 22.729.
Step-by-step explanation:
Let be [tex]a=m\cdot g -\frac{k\cdot v^{2}}{m}[/tex], the variable [tex]v[/tex] is now cleared:
[tex]\frac{k\cdot v^{2}}{m}=m\cdot g -a[/tex]
[tex]k\cdot v^{2} = m^{2}\cdot g- m\cdot a[/tex]
[tex]v^{2} = \frac{m^{2}\cdot g - m\cdot a}{k}[/tex]
[tex]v =\pm \sqrt{\frac{m^{2}\cdot g-m\cdot a}{k} }[/tex]
If [tex]a = 2.8[/tex], [tex]m=12[/tex], [tex]g = 9.8[/tex] and [tex]k = \frac{8}{3}[/tex], the value of [tex]v[/tex] is:
[tex]v=\pm \sqrt{\frac{(12)^{2}\cdot (9.8)-(12)\cdot (2.8)}{\frac{8}{3} } }[/tex]
[tex]v \approx \pm 22.729[/tex]
The value of [tex]v[/tex] is ± 22.729.
