To calculate the wavelength of an object with mass and velocity, we can use the de Broglie wavelength equation, which relates the momentum of a particle to its wavelength:
λ = h / p,
where: λ is the wavelength, h is the Planck's constant (approximately 6.626 × 10^(-34) J·s), p is the momentum of the object.
The momentum of an object is given by:
p = m * v,
where: m is the mass of the object, and v is its velocity.
Given that the mass (m) is 4 kg and the velocity (v) is 10^3 (m/s), we can calculate the momentum:
p = m * v = 4 kg * 10^3 m/s = 4000 kg·m/s.
Now, we can substitute the momentum value into the de Broglie wavelength equation:
λ = h / p = 6.626 × 10^(-34) J·s / 4000 kg·m/s.
Calculating this expression:
λ ≈ 1.6565 × 10^(-37) m.
Therefore, the wavelength of the object with a mass of 4 kg and a velocity of 10^3 m/s is approximately 1.6565 × 10^(-37) meters.