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

A

Explanation

Differentiating the equation of the curve w.r.t. `t` we get, `2((dx)/(dt))^(2)=500xx(d^(2)y)/(dt^(2))` or `(d^(2)y)/(dt^(2))=(2xx10^(4))/500=4g`, the effective `g=5g`