An SUV of mass 2200 kg,moving with a speed of 35 m/s on the highway,passes a car with the mass 1500 kg and a kinetic energy equal to that of the SUV.The ratio of the momentum of the car relative to that of the SUV is
A)0.75
B)0.83
C)0.46
D)1.0
E)0.68

Question

Quizplus · Accepted Answer

The kinetic energy of an object can be calculated as:

K = 1/2 * m * v^2

where,
K = kinetic energy
m = mass of the object
v = velocity of the object

Let the velocity of the car be v2 and its momentum be p2.

Given:
mass of SUV, m1 = 2200 kg
velocity of SUV, v1 = 35 m/s
mass of car, m2 = 1500 kg
kinetic energy of car = kinetic energy of SUV

Therefore,

1/2 * m1 * v1^2 = 1/2 * m2 * v2^2

v2 = sqrt(m1/m2) * v1

p1 = m1 * v1
p2 = m2 * v2 = m2 * (sqrt(m1/m2) * v1) = sqrt(m1 * m2) * v1

Ratio of momentum of car to that of SUV
p2/p1 = sqrt(m1 * m2) * v1 / (m1 * v1) = sqrt(m2/m1) = sqrt(1500/2200) = 0.83

Therefore, the ratio of momentum of the car to that of the SUV is 0.83. Answer choice B is correct.

An SUV of Mass 2200 Kg,moving with a Speed of 35