Question

question 25 of 25
a 2,400 kg car drives north toward a 60 kg shopping cart that has a velocity of zero. the two objects collide, giving the car a final velocity of 4.30 m/s north and the shopping cart a velocity of 8.88 m/s north. what was the initial velocity of the car?
a. 4.55 m/s south
b. 4.55 m/s north
c. 1.01 m/s north
d. 1.01 m/s south

Explanation:

Step1: Apply conservation of momentum

$m_1u_1 + m_2u_2=m_1v_1 + m_2v_2$ where $m_1 = 2400$ kg (mass of car), $m_2=60$ kg (mass of shopping - cart), $u_2 = 0$ m/s (initial velocity of shopping - cart), $v_1 = 4.30$ m/s (final velocity of car), $v_2 = 8.88$ m/s (final velocity of shopping - cart), and $u_1$ is the initial velocity of the car we want to find.

Step2: Substitute values into formula

$2400\times u_1+60\times0 = 2400\times4.30+60\times8.88$
$2400u_1=2400\times4.30 + 60\times8.88$

Step3: Calculate the right - hand side

$2400\times4.30=10320$ and $60\times8.88 = 532.8$
$2400u_1=10320 + 532.8=10852.8$

Step4: Solve for $u_1$

$u_1=\frac{10852.8}{2400}=4.522\approx4.55$ m/s. Since the final velocities of both the car and the shopping - cart are north, the initial velocity of the car is also north.

Answer:

B. 4.55 m/s north