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.
simple diagram to illustrate the setup for each law- coulombs law and biot savart law
A circular coil with 100 turns and a radius of 0.05 m is placed in a magnetic field that changes at auniform rate from 0.2 T to 0.8 T in 0.1 seconds. The plane of the coil is perpendicular to the field.• Calculate the induced electric field in the coil.• Calculate the current density in the coil given its conductivity σ.
An L-C circuit has an inductance of 0.410 H and a capacitance of 0.250 nF . During the current oscillations, the maximum current in the inductor is 1.80 A . What is the maximum energy Emax stored in the capacitor at any time during the current oscillations? How many times per second does the capacitor contain the amount of energy found in part A? Please show all steps.
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