Question

Early test flights for the space shuttle used a "glider" (mass of 980 kg including pilot). After a horizontal launch at 440 km/h from a height of 4000 m, the glider eventually landed at a speed of 210 km/h

Part A

What would its landing speed have been in the absence of air resistance?

Part B

What was the average force of air resistance exerted on it if it came in at a constant glide of 12∘∘ to the Earth?

Answer 1

a )

using equation

v_y² = u_y² + 2 g h

= 0 + 2 x 9.8 x 4000

v_y² = 78400

v_y = 280 m/sec

v_x = u_x + g t

= 440 km/h

= 122.22 m/sec

v = (v_x² + v_y²)^1/2

= ( 122.22² + 280² )^1/2

v = 305.512 m/sec

b )

let, point of starting of flight A, base point of altitude B, landing point C.

AB = 4000 m,

BC = AB / tan12

= 18818.52

v_y = v_x tan12

v = (v_x² + v_y²)^1/2

= v_x²(1+tan² 12)

= 1.045 v_x²

v = 210 km/h

= 58.33 m/s

58.33 = 1.045 v_x

v_x = 55.818 m/s

and

v_y = v_x tan12

= 11.864 m/sec

v_x² = u_x² - 2 a s

55.818² = 122.22² - 2 x a x 18818.52

a = 0.314 m/sec²

now

v_y² = u_y² + 2 b h

11.864 ² = 0 + 2 x b x 4000

b = 0.01759 m/sec²

c = g - b

= 9.8 - 0.01759

c = 9.782 m/sec²

d = ( a² + c² )^1/2

= ( 0.314² + 9.782² )^1/2

d = 9.787 m

F = m d

F = 980 x 9.787

F = 9591.2976 N

resistant force F=md=9805.3 N