Two-Dimensional Kinematics: Weightless

[r34racer01]

Early in the space program a jet aircraft was used to simulate "weightless" space flight. Beginning from a comfortable cruising altitude, assume such a craft could reach a speed of v = 590 m/s at an angle q = 31.4° above the horizontal. Subsequently the engines were used only to overcome air friction, and the plane followed a "free fall" path.

a)How long could "weightlessness" experiments be done before the plane fell back to its original altitude? t=62.7

b)How far would the plane travel horizontally during this time? x= 31575.4

c)What is the maximum height that the plane would reach above its cruising altitude?
y= 4816.11

d)What is the radius of curvature of the path at its apex?

(i.e., what is the radius of a circular path having the same velocity and acceleration as the plane at its highest point?)


Part d) is where I get stuck. The help portion says, "Use the definition of angular acceleration." So if I use a = v^2 / r and account for the horizontal velocity it should be
R = (590 cos 31.4)^2 / 9.81 = 35475.19 but apparently that's wrong. Can someone help me out?

 

[kuruman]

Redo the calculation. I used your numbers as you have them and did not get 35475.19. Hint: Set you calculator to "Degrees".

 

[r34racer01]

Redo the calculation. I used your numbers as you have them and did not get 35475.19. Hint: Set you calculator to "Degrees".

Oh wow it was in radians, jeez I'm stupid, thanks I got the right answer now.