Collision Course A useful rule of thumb in piloting is that if the heading from your airplane to a second airplane remains constant, the two airplanes are on a collision course. Consider the two airplanes shown in Figure 4-33 . At time t = 0 airplane 1 is at the location ( X , 0) and moving in the positive y direction; airplane 2 is at (0, Y ) and moving in the positive x direction. The speed of airplane 1 is v 1 . (a) What speed must airplane 2 have if the airplanes are to collide at the point ( X , Y )? (b) Assuming airplane 2 has the speed found in part (a), calculate the displacement from airplane 1 to airplane 2, Δ r → = r → 2 − r → 1 . (c) Use your results from part (b) to show that ( Δ r ) y / ( Δ r ) x = − Y / X , independent of time. This shows that Δ r → = r → 2 − r → 1 maintains a constant direction until the collision, as specified in the rule of thumb. Figure 4-33 Problem 81
Collision Course A useful rule of thumb in piloting is that if the heading from your airplane to a second airplane remains constant, the two airplanes are on a collision course. Consider the two airplanes shown in Figure 4-33 . At time t = 0 airplane 1 is at the location ( X , 0) and moving in the positive y direction; airplane 2 is at (0, Y ) and moving in the positive x direction. The speed of airplane 1 is v 1 . (a) What speed must airplane 2 have if the airplanes are to collide at the point ( X , Y )? (b) Assuming airplane 2 has the speed found in part (a), calculate the displacement from airplane 1 to airplane 2, Δ r → = r → 2 − r → 1 . (c) Use your results from part (b) to show that ( Δ r ) y / ( Δ r ) x = − Y / X , independent of time. This shows that Δ r → = r → 2 − r → 1 maintains a constant direction until the collision, as specified in the rule of thumb. Figure 4-33 Problem 81
Collision Course A useful rule of thumb in piloting is that if the heading from your airplane to a second airplane remains constant, the two airplanes are on a collision course. Consider the two airplanes shown in Figure 4-33. At time t = 0 airplane 1 is at the location (X, 0) and moving in the positive y direction; airplane 2 is at (0, Y) and moving in the positive x direction. The speed of airplane 1 is v1. (a) What speed must airplane 2 have if the airplanes are to collide at the point (X, Y)? (b) Assuming airplane 2 has the speed found in part (a), calculate the displacement from airplane 1 to airplane 2,
Δ
r
→
=
r
→
2
−
r
→
1
. (c) Use your results from part (b) to show that
(
Δ
r
)
y
/
(
Δ
r
)
x
=
−
Y
/
X
, independent of time. This shows that
Δ
r
→
=
r
→
2
−
r
→
1
maintains a constant direction until the collision, as specified in the rule of thumb.
20. Two small conducting spheres are placed on top of insulating pads. The 3.7 × 10-10 C sphere is fixed whie
the 3.0 × 107 C sphere, initially at rest, is free to move. The mass of each sphere is 0.09 kg. If the spheres
are initially 0.10 m apart, how fast will the sphere be moving when they are 1.5 m apart?
Biology: Life on Earth with Physiology (11th Edition)
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