If x=2+3√2, then find the value of x+1/2
Answers
Answer:
\blue{\bold{\underline{\underline{Answer:}}}}
Answer:
\green{\tt{\therefore{Maximum\:height=26.67\:m}}}∴Maximumheight=26.67m
\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}
Step−by−stepexplanation:
\begin{lgathered}\green{\underline \bold{Given:}} \\ \tt: \implies Velocity \: at \: one \: fourth = 20 \: m/s \\ \\ \red{\underline \bold{To \: Find:}}\\ \tt: \implies Maximum \: height \: attained = ?\end{lgathered}
Given:
:⟹Velocityatonefourth=20m/s
ToFind:
:⟹Maximumheightattained=?
• According to given question :
\begin{lgathered}\tt \circ \: Let \: height \: be \: h \\ \\ \tt \circ \: Final \: velocity = 20 \: m/s \: at \: \frac{h}{4} \\ \\ \tt \circ \: Acceleration = - 10 \: {m/s}^{2} \\ \\ \bold{As \: we \: know \: that : } \\ \tt: \implies {v}^{2} = {u}^{2} + 2as \\ \\ \tt: \implies {20}^{2} = {u}^{2} + 2 \times ( - 10) \times \frac{h}{4} \\ \\ \tt: \implies 400 = {u}^{2} - 5h \\ \\ \tt: \implies {u}^{2} = 400 + 5h - - - - - (1) \\ \\ \tt \circ \: Final \: velocity = 0 \: m/s \: \: \: (For \: maximum \: height) \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies {v}^{2} = {u}^{2} + 2as \\ \\ \tt: \implies {0}^{2} = {u}^{2} + 2 \times ( - 10) \times h \\ \\ \tt: \implies 0 = {u}^{2} - 20h \\ \\ \tt: \implies {u}^{2} = 20h - - - - - (2) \\ \\ \circ \: \tt{Putting \: value \: of \: {u}^{2} \: in \: (1)} \\ \tt: \implies 20h = 400 + 5h \\ \\ \tt: \implies 15h = 400 \\ \\ \tt: \implies h = \frac{400}{15} \\ \\ \green{\tt: \implies h = 26.67 \: m} \\ \\ \green{\tt \therefore Maximum \: height \: attained \: is \: 26.67 \: m}\end{lgathered}
∘Letheightbeh
∘Finalvelocity=20m/sat
4
h
∘Acceleration=−10m/s
2
Asweknowthat:
:⟹v
2
=u
2
+2as
:⟹20
2
=u
2
+2×(−10)×
4
h
:⟹400=u
2
−5h
:⟹u
2
=400+5h−−−−−(1)
∘Finalvelocity=0m/s(Formaximumheight)
Asweknowthat
:⟹v
2
=u
2
+2as
:⟹0
2
=u
2
+2×(−10)×h
:⟹0=u
2
−20h
:⟹u
2
=20h−−−−−(2)
∘Puttingvalueofu
2
in(1)
:⟹20h=400+5h
:⟹15h=400
:⟹h=
15
400
:⟹h=26.67m
∴Maximumheightattainedis26.67m
Answer:
putting the value of x in x+1/2
2+3√2+1/2=2(2+3√2)/2+1/2
=4+6√2/2+1/2=5+6√2/2
therefore x+1/2=5+6√2/2