A 120-kg roller coaster cart is being tested on a new track, and a crash-test dummy is loaded into it. The roller coaster starts from rest at point A which is 35 m above the ground. The cart is observed to roll down the track to point B, which is 10 m above the ground. In your own words, what physics ideas would you be able to use to predict how fast the cart is moving at point B? What calculations would you use, what things would you be measuring, and what physics principles or laws would you use to make this calculation?

v₂ = 22.13 m/s

We need to measure heights of both points and the law of conservation of energy is applied to measure this speed.

Explanation:

In order to find the speed at the point B, we will use the Law of conservation of energy between points A and B to get the required results, as follows:

Total Energy of Cart at Point A = Total Energy of Cart Point B

K.E at A + P.E at A = K.E at B + P.E at B

(1/2)mv₁² + mgh₁ = (1/2)mv₂² + mgh²

(1/2)m(v₁² - v₂²) = mg(h₂ - h₁)

(1/2)(v₁² - v₂²) = g(h₂ - h₁)

where,

v₁ = velocity of cart at Point A = 0 m/s

v₂ = Velocity of Cart at Point B = ?

h₁ = height of point A relative to the ground = 35 m

h₂ = height of point B relative to the ground = 10 m

g = 9.8 m/s²

Therefore,

(1/2)[(0 m/s)² - v₂²] = (9.8 m/s²)(10 m - 35m)

- v₂² = - (2)(245 m²/s²)

v₂ = √(490 m²/s²)

v₂ = 22.13 m/s

We need to measure heights of both points and the law of conservation of energy is applied to measure this speed.

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