Please solve this and find the value of X A 1400 kg car moving at 18 m/s approac

Question

Please solve this and find the value of X

A 1400 kg car moving at 18 m/s approaches a hill that is 25 m high and 31 m long. Although the car and hill are clearly too large to be treated as matter waves, determine what the equation T?e-2bL, where m is the mass, L is the barrier thickness, Ub - E is the energy difference and h is the Planck constant, predicts for the transmission coefficient of the car, as if it could tunnel through the hill as a matter wave. Treat the hill as a potential energy barrier where the potential energy is gravitational. Write your answer as T=ex and find the value of x. Please solve this and find the value of X

Explanation / Answer

tunneling probability T = e^-2kL

where k =2*pie* sqrt[2m(U-E)]/h

so according to your question

X =-4*pie*sqrt[2m(U-E)]*L/h

where h is plankc constant.

the gravitational potential is

U=-GM/(r+h)

where r is radius of the earth and h is the height of the hill

U=6.25*10^7

E=(mv^2)/2

= 2.2*10^5

hence U-E= 62.28*10^6

k=2*3.14*sqrt[2*1400*62.28*10^6]/6.626*10^-34

=2*3.14*417593/6.626*10^-34

=3.95*10^39

X=-2kL

=-2*3.95*10^39*31

=-2.449*10^41

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