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A 910-kg sports car collides into the rear end of a 2100-kg SUV stopped at a red light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.7 m before stopping. The police officer, estimating the coefficient of kinetic friction between tires and road to be 0.80, calculates the speed of the sports car at impact. What was the speed sports car at impact?

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Answer:

The speed of the sports car at impact is 21.52 m/s

Explanation:

Given;

mass of sport car, m₁ = 910-kg

mass of SUV, m₂ = 2100-kg

Coefficient of kinetic friction = 0.80

distance moved by the cars before stopping, s = 2.7 m

let the speed of the sport car at impact be u₁

Also, let the speed of the SUV at impact be u₂

The deceleration of the cars after the impact can be calculated using frictional force formula;

[tex]F_k = \mu N\\\\(m_1 +m_2)(-a) = \mu g(m_1 +m_2)\\\\a = - \frac{\mu g(m_1 + m_2)}{(m_1 + m_2)} \\\\a = -\mu g\\\\a = -(0.8 *9.8)\\a = -7.84\ m/s^2[/tex]

The common velocity of the cars after the impact can be calculate using kinematic equation

v² = u² + 2as

0 = u² + (2 x -7.84 x 2.7)

0 = u² - 42.336

u² = 42.336

u = √42.336

u = 6.507 m/s

Finally, we determine the speed of the sports car at impact by applying principle of conservation of linear momentum;

Total momentum before collision = Total momentum after collision

m₁u₁ + m₂u₂ = u(m₁ + m₂)

Since the SUV stopped at a red light, u₂ = 0

910u₁ + 0 = 6.507(910 + 2100)

910u₁ = 19586.07

u₁ = 19586.07 / 910

u₁ = 21.52 m/s

Thus, the speed of the sports car at impact is 21.52 m/s