A sprinter must average 24.0 mi/h to win a 100-m dash in 9.30 s. What is his wavelength at this speed if his mass is 84.5 kg? A)7.29 × 10 ⁻³⁷ m B)3.26 × 10 ⁻³⁷ m C)5.08 × 10 ⁻³⁰ m D)1.34 × 10 ⁻³⁰ m E)None of these choices are correct.

Question

Quizplus · Accepted Answer

We can use the formula λ = h/mv, where h is Planck's constant, m is the mass of the object in motion, v is the velocity, and λ is the wavelength. 
First, we need to convert the speed to m/s: 
24.0 mi/h = (24.0 mi/h)(1.609344 km/mi)(1000 m/km)(1 h/3600 s) = 10.67 m/s
Now we can solve for the wavelength: 
λ = (6.626 x 10^-34 J*s)/(84.5 kg)(10.67 m/s) = 7.29 x 10^-9 m = 7.29 nm 
Therefore, the answer is choice A.

A Sprinter Must Average 24