Question

A typical meteor that hits the earth’s upper atmosphere has a mass of only 2.5 g, about the same as a penny, but it is moving at an impressive 40 km/s. As the meteor slows, the resulting thermal energy makes a glowing streak across the sky, a shooting star. The small mass packs a surprising punch. At what speed would a 900 kg compact car need to move to have the same kinetic energy

Answer 1

Answer:

v = 67 m/s

Explanation:

The meteor has a mass (m) of 2.5 g and a speed (v) of 40 km/s. In SI units:

2.5 g × (1 kg / 10³ g) = 2.5 × 10⁻³ kg

40 km/s × (10³ m / 1 km) = 4.0 × 10⁴ m/s

The kinetic energy (KE) is:

KE = 1/2 × m × v² = 1/2 × (2.5 × 10⁻³ kg) × (4.0 × 10⁴ m/s)² = 2.0 × 10⁶ J

A 900 kg compact car, with the same kinetic energy, must have the following speed.

KE = 1/2 × m × v²

2.0 × 10⁶ J = 1/2 × 900 kg × v²

v = 67 m/s

Answer 2

Answer:u=66.67 m/s

Explanation:

Given

mass of meteor $m=2.5 gm\approx 2.5\times 10^{-3} kg$

velocity of meteor $v=40km/s \approx 40000 m/s$

Kinetic Energy of Meteor

$K.E.=\frac{mv^2}{2}$

$K.E.=\frac{2.5\times 10^{-3}\times (4000)^2}{2}$

$K.E.=2\times 10^6 J$

Kinetic Energy of Car

$=\frac{1}{2}\times Mu^2$

$=\frac{1}{2}\times 900\times u^2$

$\frac{1}{2}\times 900\times u^2=2\times 10^6$

$900\times u^2=4\times 10^6$

$u^2=\frac{4}{9}\times 10^4$

$u=\frac{2}{3}\times 10^2$

$u=66.67 m/s$