Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

A 750 kg car is stalled on an icy road during a snowstorm. A 1000 kg car traveling eastbound at 13 m/s collides with the rear of the stalled car. After being hit, the 750 kg car slides on the ice at 4 m/s in a direction 30 ∘ north of east.
A) What is the magnitude of the velocity of the 1000 kg car after the collision?
B) What is the direction of the velocity of the 1000 kg car after the collision?
C) Calculate the ratio of the kinetic energy of the two cars just after the collision to that just before the collision. (You may ignore the effects of friction during the collision.)

Sagot :

onyebuchinnaji

(a) The magnitude of the velocity of the 1000 kg car after the collision is 10.5 m/s.

(b) The direction of the velocity of the 1000 kg car after the collision is 8.2 ⁰ north west.

(c) The ratio of the kinetic energy of the two cars just after the collision to that just before the collision is 0.72.

Velocity of the 1000 kg after the collision

Apply the principle of conservation of linear momentum as follows;

Final velocity in x direction

m₁u₁  +  m₂u₂ = m₁v₁x  +  m₂v₂x

where;

  • m₁ is mass of 750 kg car
  • u₁ is initial velocity of 750 kg mass
  • m₂ is mass of 1000 kg car
  • u₂ is initial velocity of 1000 kg mass
  • v₁ is final velocity of 750 kg mass
  • v₂ is final velocity of 1000 kg mass

750(0) + 1000(13) = 750(4 cos 30)   +   1000v₂x

13000 = 2,598.1  +   1000v₂x

10,401.9 = 1000v₂x

v₂x  =  10.4 m/s

Final velocity in y direction

m₁u₁  +  m₂u₂ = m₁v₁y  +  m₂v₂y

750(0) + 1000(0) = 750(4 sin 30)   +   1000v₂y

0 = 1500 +  1000v₂y

v₂y  = -1500/1000

v₂y  = -1.5 m/s

Resultant final velocity

v = √(v₂ₓ² + v₂y²)

v = √[(10.4)² + (-1.5)²]

v = 10.5 m/s

Direction of the final velocity of 1000 kg car

tanθ = v₂y/v₂ₓ

tanθ = -1.5/10.4

tanθ =  -0.144

θ = arc tan(-0.144)

θ = 8.2 ⁰ north west

Kinetic energy of the cars before the collision

K.Ei = 0.5m₁u₁²  +  0.5m₂u₂²

K.Ei = 0.5(750)(0)²  +  0.5(1000)(13)²

K.Ei = 84,500 J

Kinetic energy of the cars after the collision

K.Ef = 0.5(750)(4)²  +  0.5(1000)(10.5)²

K.Ef = 61,125 J

Ratio of the kinetic energy

K.Ef/K.Ei = 61,125/84,500

K.Ef/K.Ei = 0.72

Thus, the magnitude of the velocity of the 1000 kg car after the collision is 10.5 m/s.

The direction of the velocity of the 1000 kg car after the collision is 8.2 ⁰ north west.

The ratio of the kinetic energy of the two cars just after the collision to that just before the collision is 0.72.

Learn more about kinetic energy here: https://brainly.com/question/25959744

#SPJ1

We appreciate your time. Please come back anytime for the latest information and answers to your questions. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.