A plane flies with a constant velocity of 208 m/s. The clocks on the plane show that it takes exactly 2.00 hours to travel a certain distance. Calculate how much longer or shorter than 2.00 h this flight will last, according to clocks on the ground. ________s
delta t = delta t(not) / (1-v^2/c^2)
The Attempt at a Solution
Because the velocity of the plane is very low, I used the binomial expansion: delta t = delta t(not)*[1 + 1/2*[208m/s / 3x10^8 m/s]^2]. When I worked it out and solved for delta t, I got .999, which I then added to the 7200s ( 2 hours). I know that the time according to the ground clocks will be longer, but I think there's a math error somewhere which is preventing me from understanding and getting the answer. Any help is appreciated. Thank you!