Rita Skeeter goes boom

The Law of Conservation of Momentum states:

$m \times v$ = constant , where m is mass, and v is velocity.

The mass of the woman is 70 kg , and the velocity is 1 m/s . The woman is transformed to a beetle that is 10 g . 10 g = 0.01 kg . You then need to find the velocity after the transformation.

$(70 kg) \times (1 m/s)$ = $(0.01 kg) \times (v)$ Solve for v

v = $\frac{70}{0.01}$ v = 7,000 m/s

The question asks for how many times faster than the speed of sound is this. The speed of sound is given as 340 m/s . So take $\frac{7000}{340}$ which gives 20.5882

By Law of Conservation of Momentum we have, momentum before transformation = momentum after transformation (70 kg)(1m/s) = (0.01kg) Velocity after transformation Velocity = (70kgm/s)/ 0.01kg Velocity = 7000m/s

(7000m/s)/ (340m/s) = 20.588

That is 20.588 times faster than the speed of sound.

The momentum of the body before and after the collision is equal due to the principle of linear momentum. mass of the woman=70 kg (m 1) velocity of it=1m/s(u 1) mass of the beetle=10g or 0.01kg(m 2) velocity=?(u 2) => m 1*u 1=m 2*u 2 70/.01=u 2 7000m/s=u 2 therefore the speed of the beetle is 7000m/s speed of sound is 340m/s => 340x=7000 x=7000/340 x=20.5882 (approx.)

As the woman reduces her mass into a mass of a beetle, her momentum is still conserved. If m1 is the mass of the woman =70 kg, v1 the speed of the woman = 1 m/s, m2 the mass of the beetle = 10 g = 0.01kg and v2 the speed of the beetle which is UNKNOWN; then; m1v1 = m2v2 (70kg)(1m/s) = (0.01kg)(v2) then; v2 = 7,000 m/s

Divide v2 by the speed of sound: 7,000 m/s / 340 m/s = 20.59

We know that according to the law of conservation of momentum (the product of mass and velocity); the initial momentum of a system is equal to the final momentum provided net external force on the system remains zero.

Hence, Let initial mass of the body be m, velocity be v, and final mass and velocity to be M and V, then m v = M V Solving we get V = 7000 m/s

So , no. of times faster than sound = 7000/340 = 20.6

The momentum of the woman is given by $p=mv$ . This tells us that the woman's momentum is $70kg\cdot m/s$ . Since the momentum is conserved when she becomes a beetle, we know that $70kg\cdot m/s=10g\cdot v$ , which tells us that the beetle's velocity is $7000m/s$ . $(7000m/s)/(340m/s)=20.59$ . Thus, she is 20.59 times faster than the speed of sound.

Momentum = mass x velocity. Thus the momentum of the woman = 70000 g x 1 m/s = 70000 mg/s. When she changes into a beetle her velocity = momentum/mass = 70000mg/s/10g = 7000 m/s. this is approximately 20.59 times faster than the speed of sound.