An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

Options

A. 1m
B. 1.26 m
C. 1.46 m
D. 1.56 m

Answer

D

Explanation

Cleary, equation of ellipse takes the from `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` here, it is given that 2a = 8 and b=2 `
`rArr a=4 and b=2` put the values of a and b in eq. (i), we get `x^(2)/(16)+(y^(2))/(4)=1` given, ap=1.5 m `
`rArr op= oa-ap=4-1.5
` op= 2.5 m let pq=k then, the coordinate q(2.5,k) will satisfy the equatin of ellipse. i.e. `(2.5^(2))/(16)+(k^(2))/(4)=1rArr(6.25)/(16)+k^(2)/(4)=1`
`rArrk^(2)/(4)=(1)/(1)-(6.25)/(16)=(16-625)/(16)`
`rArrk^(2)/(4)=(9.75)/(16) rArrk^(2)=(9.75)/(4)`
`rArrk^(2)=2.4375`
` therefore k=1.56 m (approx.)`