Question

A grocery shopper tosses a(n) 8.9 kg bag of

Answer 1

The final speed of the cart and the bag is 1.9 m/s

Explanation:

We can solve the problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the system must be conserved before and after the collision.

Therefore, we can write:

$p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v$  

where:  

$m_1 = 8.9 kg$ is the mass of the bag

$u_1 = 5.7 m/s$ is the initial velocity of the bag

$m_2 = 18.4 kg$ is the mass of the cart

$u_2 = 0$ is the initial velocity of the cart (which is stationary)

$v$ is the final combined velocity of the cart with the bag

Re-arranging the equation and substituting, we find the final combined velocity (and speed):

$v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{(8.9)(5.7)+0}{8.9+18.4}=1.9 m/s$

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