The US military is running tests on a new ultrafast plane to see how fast it can

Question

The US military is running tests on a new ultrafast plane to see how fast it can go. They set up a pair of beacons 15000 km apart, and time how long it takes the plane to fly horizontally between them. 5. A person on the ground measures 1s between the plane passing the first beacon and the plane passing the second beacon. How fast is the plane going? How far apart does a person on the plane think the beacons are? Assume the person on the plane is 6' tall, and they're standing up as they pass a person on the ground. If the person on the ground can measure the height of the person on the plane, do they measure them as 6' tall? If not, what height do they measure? a. b. c.

Explanation / Answer

(a) distance between two beacon = 15000km = 1.5*106 m

time taken to cover this distance = 1 sec

so speed of ship = distance/time = 1.5*106 m/sec

(b) length measured by moving observer

L = Lo(1 - v2/c2)0.5

L = 15000(1 - (1.5*106/3*108)2)0.5

L = 14999.81 km

(c)

person standing on ground will measure more than 6 ft. by relativity

length measured by person on ground = 6/(1 - v2/c2)

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