In order to simulate different values of `g` aspiring astronauts are put on a plane which dives in a parabola given by the equation `x^2 = 500y`. Where `x` is horizontal, `y` is vertically upwards, both being measured in meter. The `x`-component of the velocity of the plane is constant throughout, and has the value of `360 km//h`. the effective `g`("g-force") experienced by an astronaut on the plane equals

Options

A. 4g
B. 3g
C. `(g)/(5) `
D. 5g

Answer

D

Explanation

Differentiating the equation of the curve w.r.t we get ,
`2 ((dx)/(dt))^(2) = 500 xx (d^(2)y)/(dt^(2))`
or, `(d^(2)y)/(dt^(2)) = (2 xx 10^(4))/(500) = 4g`. The effective .g. = 5g.