Question

As preparation for this problem, review Conceptual Example 10. The drawing shows two planes each about to drop an empty fuel tank. At the moment of release each planehas the same speed of 130 m/s, and each tank is at the same height of 2.00 km above the ground. Although the speeds are the same, the velocities are different at theinstant of release, because one plane is flying at an angle of 15.0° above the horizontal and the other is flying at an angle of 15.0° below the horizontal. Find themagnitude and direction of the velocity with which the fuel tank hits the ground if it is from each plane. Give the directional angles with respect to thehorizontal.

(a) plane A
Magnitude m/s
Direction ° below the horizontal


(b) plane B
Magnitude m/s
Direction ° below the horizontal

Answer 1

:

Plane A
Magnitude - 275 m/s
Direction - 62.9 ° below horizontal

Plane B
Magnitude - 275 m/s
Direction - 62.9 ° below horizontal

Answer 2

Plane A (flying at 15° above horizontal):

initial vertical velocity = 130*sin(15)
initial horizontal velocity = 130*cos(15)

v² = u² + 2as

vertically : v² = (130*sin(15))² + 2(-9.8)(-3000) = 59932.09...

v = ±244.81 m/s (2dp)

velocity vertically is downwards as it has fallen, so take the negative value.

horizontally, v = u, as no acceleration horizontally, so v = 130*cos(15) = 125.57 m/s (2dp)

magnitude = v(244.81² + 125.57²) = v(75700) = 275 m/s (3sf)

direction = tan^-1 (-244.81/125.57) = -62.9 ° (3sf)

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Plane B (flying at 15° below horizontal):

This will be the same as above, as the velocity of the tank will be the same at the height of release, regardless of whether it was initially travellingupwards or downwards to start with. Therefore the tanks will hit the ground with the same velocity, so even the direction of the tanks when they hit theground will be the same. The only difference in the 2 situations is the distance travelled by each tank, with the one initially travelling upwards withtravel further.