Johnny Jumper\'s favorite trick is to step out of his 16^th- story window and fa

Question

Johnny Jumper's favorite trick is to step out of his 16^th- story window and fall 50.0 m into a pool. A news reporter takes a picture of 75.0-kg Johnny just before he makes a splash, using an exposure time of 5.00ms. Find a) Johnny's de Broglie wavelength at this moment, b) the uncertainty of his kinetic energy measurement during such a period of time, c) the present error caused by such an uncertainty, d) at what speed will a 10% uncertainty arise, and e) what mass does the planet have to be to cause this speed?

Explanation / Answer

a) De broglie wavelegth = h/mv = 6.623 x 10-34 / 75 x (root( 2x 9.8x50) ( Here v = root( 2 gh) )

=2.76 x 10-34 m

b) time to fall =3.194 (+/-) 0.005

Variation in velocity= (31.35 , 31.25)

variation in kinetic energy = 1/2 x75 ( 982.8 - 976.56)

Uncertainity =234 J

C) percent error = 234/36750 = 0.636%

d) if velocity is 2m/s then there will 10% increase in uncertainity, higher the velocity leser is the uncerrtaininty

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