Superluminal jets figure a shows the path taken by a knot in a jet of ionized gas that has been expelled from a galaxy. The knot travels at constant velocity i at angle θ from the direction of Earth. The knot occasionally emits a burst of light, which is eventually detected on Earth. Two bursts are indicated in Figure a, separated by time t as measured in a stationary frame near the bursts. The bursts are shown in Figure b as if they were photographed on the same piece of film, first when light from burst L arrived on Earth and then later when light from burst 2 arrived. The apparent distance D app traveled by the knot between the two bursts is the distance across an Earth-observer's view of the knot's path. The apparent time Tapp, between the bursts is the difference in the arrival times of the light from them. The apparent speed of the knot is then Vapp = Dapp/Tapp. In terms of v, t, and g, what are?

(a) Dapp and

(b) Tapp?

(c) Evaluate Vapp for v = 0.980c and θ = 30.0o. When superluminal (faster than light) jets were first observed, they seemed to defy special relativity-at least until the correct geometry (Figure a) was understood.