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In an action movie, a spy is lying still on top of a train. The train is moving at a speed of 95 km/h. Three bad guys are after the spy. One is in a helicopter flying above the train and moving at the same speed in the same direction as the train. The second is a spotter sitting above a tunnel opening that the train is headed for. The third is in a car that is driving alongside the train, in the opposite direction, at a speed of 105 km/h. Which statement is supported by this scenario? The person in the car and the spotter above the tunnel will both observe the speed of the person on the train as 95 km/h. The person in the helicopter and the spotter above the tunnel will both observe the speed of the person on the train as 95 km/h. The spotter above the tunnel will observe the speed of the spy as 95 km/h, and the person in the car will observe the speed of the spy as 200 km/h. The person in the helicopter will observe the speed of the spy as 95 km/h, and the person in the car will observe the speed of the spy as 105 km/h.

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This specific question applies the concept of relative velocity. Relative velocity is describes as the velocity of an object with respect to another object, whether static or moving. For this problem, the correct statement is the spotter above the tunnel will observe the speed of the spy as 95 km/h, and the person in the car will observe the speed of the spy as 200 km/h. The following are the justification, relative speed of the spotter at the tunnel is equal to velocity (Vss) = velocity spy relative to the ground (Vsg)  + V ground relative to the spotter (Vgs). Thus, V = 95 + 0 km/h = 95 km/h. Note that the sign of velocity is dependent on the direction, hence, opposite direction is equal to negative velocity. For the second condition, velocity of the spy in reference person in the car is equal to velocity of the spy reference to ground plus the velocity of the ground reference to the person in the car. Thus, V = 95 km/h + 105 km/h = 200 km/h. Please be cautious in assigning the sign of the velocity.

Answer:

The spotter above the tunnel will observe the speed of the spy as 95 km/h, and the person in the car will observe the speed of the spy as 200 km/h

Explanation:

Velocity of spy is 95 km/h in the direction of train

Helicopter is flying above the train with same speed as that of train

so here by the concept of relative velocity

[tex]v_{TH}[/tex] = velocity of train with respect to helicopter

[tex]v_{TH} = v_T - v_H[/tex]

[tex]v_{TH} = 95 - 95 = 0[/tex]

now we can say that as per the helicopter the spy will remain at rest

Now another guy is above a tunnel and standing there at rest

so here the guy is in stationary frame so he will observe the real speed of the spy

so as per second guy the speed of spy is 95 km/h

now third guy is inside a car moving in opposite direction of the spy

so here we have

[tex]v_{TC}[/tex] = speed of train with respect to car

[tex]v_{TC} = v_T - v_C[/tex]

[tex]v_{TC} = 95 -(-105) = 200 km/h[/tex]

so third guy will see the spy is moving towards him with speed 200 km/h

so correct answer will be

The spotter above the tunnel will observe the speed of the spy as 95 km/h, and the person in the car will observe the speed of the spy as 200 km/h

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