Question

An airplane ascends such that its gain h in altitude is proportional to the square root of the change x in horizontal distance traveled. If h=256 m for x=256 m and v Subscript x is constant at 370​ m/s, find the velocity at this point.

Answer 1

Answer:velocity=185 m/s

Step-by-step explanation:

So make k the subject of the formula by divide both by sqrt(x)

h= k × sqrt(x)

k=h/sqrt(x)

k=256 / sqrt(256)

k=256 / 16

k=16

So now substitute the value of k :

h= 16 × sqrt (x)

Then differentiate:

=(1/2 × sqrt(x))× 16

=16/(2×sqrt(x)

=8/sqrt(x)

Then

= 8/sqrt(x) × 370

=8/ sqrt(256) × 370

=8/16 × 370

velocity=185 m/s