Question

A plane is flying horizontally at height h at speed v0 = 2√2gh over the ocean in a fixed direction given by the angle φ north of east to drop a bundle of supplies to castaways on a small raft at colatitude θ < π/2. Neglect air resistance. (a) In order to land on the raft, at what time must the bundle be released, relative to when it lands on the raft, to first order in Ω, the rate of rotation of the earth? (b) In order to land on the raft, where must the plane be, relative to the raft, when the bundle is released, to first order in Ω?

Answer 1

1)velocity of plane  v0 = 2√2gh

2)aeroplane is flying horizontally at a height =h

3) I would take accelaration along y direction = g=9.8m/sec^2

Clearly it would be case of projectile motion,Refer to drawn figure

From the projectile motion we know that accleration along horizontal direction is zero i.e ax=0

Acceleration along horizontal direction equals to zero.

so, distance covered in horizontal direction , x = ut.

Here for (a) part first

so to find time taken by supplies to casteways on a small raft towards ground is with height h.

Acceleration along vertical direction,ay = g = 9.8 m/s² and =0

using formula, s = ut + 1/2 at²

h = 4.9t² => t = √(h/4.9) sec

now for (b) part

distance travelled in horizontal direction, x = ut = 2√2gh × √(h/4.9) = { 2√2gh √(h/4.9} meter