Early test lights for the space shuttle used a \'glider\' (mass of 060 kg includ

Question

Early test lights for the space shuttle used a 'glider' (mass of 060 kg including pilot) After a horizontal launch at 540 km/h from a height of 4000 m. the glider eventually landed at a speed of 210 km/h. What would its landing speed have boon in the absence of air resistance? Express your answer using two significant figures. What was the average force of air resistance exerted on it if it came in at a constant glide of 12 degree to the Earth? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

a)

we know, vy^2 = uy^2 + 2gH
= 0 + 2*9.81*4000
vy =280.14 m/s
vx = ux + gt= 540 km/h+ 0=138.89 m/s
so, v = [ vx^2 + vy^2 ]^(1/2)
= [ 138.89^2 + 280^2 ]^(1/2)
= 296.581 m/s

b)

as here air resistance is significant, projectile rules are not applicable here.
let, point of starting of flight A, base point of altitude B, landing point C.
AB=4000m, BC=AB/tan10=19849.486 m
now, at C, vy/vx = tan10
or, vy = vx tan10
but, v^2 = vx^2 + vy^2 = vx^2(1+tan^2 10)=1.031vx^2
v=210 km/h=210000/3600 m/s=55.56 m/s
so, 55.56 = 1.0154 vx
or, vx = 54.716 m/s
and vy=vxtan10=9.648 m/s
now, vx^2 = ux^2 - 2as
or, 54.716^2 = 138.89^2 - 2a*19849.486
so, a= 0.411 m/s^2
and, vy^2 = uy^2 + 2bH
or, 9.648^2 = 0 + 2b*3500
so, b=0.0133 m/s^2
resistant decceleration c=g-b=9.797 m/s
overall resistant decceleration, d = [a^2 + c^2]^(1/2)
= 9.8053 m/s^2
resistant force F=md=9805.3 N

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