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

v = 67 m/s

Step-by-step 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

Step-by-step explanation:

Given

mass of meteor
`m=2.5 gm\approx 2.5* 10^(-3) kg`

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

Kinetic Energy of Meteor

`K.E.=(mv^2)/(2)`

`K.E.=(2.5* 10^(-3)* (4000)^2)/(2)`

`K.E.=2* 10^6 J`

Kinetic Energy of Car

`=(1)/(2)* Mu^2`

`=(1)/(2)* 900* u^2`

`(1)/(2)* 900* u^2=2* 10^6`

`900* u^2=4* 10^6`

`u^2=(4)/(9)* 10^4`

`u=(2)/(3)* 10^2`

`u=66.67 m/s`