Question

In 1976, the Lockheed SR-71A Blackbird set the record speed for any airplane: 3.53*10^3 km/h. Suppose you observe this plane ascending at this speed. For 20.0 s, it flies at an angle of 15.0 degrees above the horizontal, then for another 10.0 s it's angle of ascent is increased to 35.0 degrees. Calculate the plane's total gain in altitude, it's total horizontal displacement, and its resultant displacement.

Answer 1

v = speed of motion = 3530 km/h = 3530 (1000/3600) m/s = 980.6 m/s

consider the motion when the angle with the horizontal is 15 deg :

`v_(oy)` = component of velocity along vertical direction = v Sin15 = 980.6 Sin15 = 253.8 m/s

`v_(ox)` = component of velocity along horizontal direction = v Cos15 = 980.6 Sin15 = 947.2 m/s

t = time of travel = 20 sec

X = displacement along the x-direction

Y = displacement along the Y-direction

Horizontal displacement in first 20 sec is given as

X =
`v_(ox)` t

X = 947.2 x 20

X = 18944 m

vertical displacement in first 20 sec is given as

Y =
`v_(oy)` t

Y = 253.8 x 20

Y = 5076 m

consider the motion when the angle with the horizontal is 35 deg :

`v'_(oy)` = component of velocity along vertical direction = v Sin35 = 980.6 Sin35 = 562.4 m/s

`v'_(ox)` = component of velocity along horizontal direction = v Cos35 = 980.6 Sin35 = 803.3 m/s

t = time of travel = 10 sec

X' = displacement along the x-direction

Y' = displacement along the Y-direction

Horizontal displacement in next 10 sec is given as

X' =
`v'_(ox)` t

X' = 803.3 x 10

X' = 8033 m

vertical displacement in next 10 sec is given as

Y' =
`v'_(oy)` t

Y' = 562.4 x 10

Y' = 5624 m

X'' = total horizontal displacement

Y'' = total vertical displacement

Total horizontal displacement is given as

X'' = X + X' = 18944 + 8033 = 26977 m

Total vertical displacement is given as

Y'' = Y + Y' = 5076 + 5624 = 10700 m

Total gain in altitude = Y'' = 10700 m

total horizontal displacement = X'' = 26977 m

resultant displacement using pythagorean theorem is given as

R = sqrt(X''² + Y''²)

R = sqrt((26977)² + (10700)²)

R = 29021.5 m