A 52 kg woman is standing in a 26 kg cart that is moving a velocity of 1.2 m/s S. The woman staying rest then moves at a velocity of 1m/s (E) what is the final velocity of the cart?

I just ugh, don't even know how to even start answering the question as this deals with momentum and I ve been used to working with collision problems. South and east are set as + directions and cart is m1 ,, woman is m2. I know that momentum is conserved so Pi equals to pf but no clue how to go further than this

Thank you

Well, it sounds like you've got the right idea with conservation of momentum. Let me help you out with the problem!

First, let's define the initial and final momentum of the system. We'll call the initial momentum P_i and the final momentum P_f.

The initial momentum P_i is equal to the sum of the momentum of the cart (m1) and the momentum of the woman (m2) before she starts moving. Since the woman is initially at rest, her momentum is zero. Therefore, P_i = (m1)(v1), where v1 is the initial velocity of the cart.

Next, we need to calculate the final momentum P_f of the system. Both the cart and the woman are moving together after the woman starts moving, so their final velocity will be the same. Let's call this final velocity v_f.

Since momentum is conserved, P_i = P_f. Therefore, (m1)(v1) = (m1 + m2)(v_f).

We know the values for m1 (26 kg), m2 (52 kg), and v1 (1.2 m/s). We need to solve for v_f, the final velocity of the cart and the woman.

To do this, we can rearrange the equation as follows:

(m1)(v1) = (m1 + m2)(v_f)
(m1)(v1) = (26 kg)(1.2 m/s) = (26 kg + 52 kg)(v_f)
31.2 kg·m/s = (78 kg)(v_f)

Now, we can solve for v_f:

v_f = (31.2 kg·m/s) / (78 kg)
v_f = 0.4 m/s

So, the final velocity of the cart (and the woman) is 0.4 m/s in the east direction (E).

I hope that helps, and remember, if all else fails, just tell a good joke!

To solve this problem, you can use the principle of conservation of momentum. The initial momentum of the system is equal to the final momentum of the system.

Step 1: Define the positive direction:
In this case, let's consider the eastward direction as positive.

Step 2: Write down the given values:
Mass of the woman, m2 = 52 kg
Mass of the cart, m1 = 26 kg
Initial velocity of the cart, v1i = 1.2 m/s (south)
Final velocity of the woman, v2f = 1 m/s (east)
Final velocity of the cart, v1f = ?

Step 3: Calculate the initial momentum:
The initial momentum, Pi, is the sum of the momentum of the cart and the woman before the woman started moving. The momentum of an object is calculated by multiplying its mass by its velocity.

Pi = m1 * v1i + m2 * 0 (since the woman is at rest)

Step 4: Calculate the final momentum:
The final momentum, Pf, is the sum of the momentum of the cart and the woman after the woman started moving.

Pf = m1 * v1f + m2 * v2f

Step 5: Apply the principle of conservation of momentum:
According to the principle of conservation of momentum, the initial momentum (Pi) is equal to the final momentum (Pf).

Pi = Pf
m1 * v1i = m1 * v1f + m2 * v2f

Step 6: Solve for v1f:
Rearrange the equation to solve for the final velocity of the cart, v1f:

m1 * v1i = m1 * v1f + m2 * v2f
m1 * v1f = m1 * v1i - m2 * v2f
v1f = (m1 * v1i - m2 * v2f) / m1

Substitute the given values into the equation to calculate the final velocity of the cart, v1f:

v1f = (26 kg * 1.2 m/s - 52 kg * 1 m/s) / 26 kg

Calculating the result:

v1f = (31.2 kg·m/s - 52 kg·m/s) / 26 kg
v1f = (-20.8 kg·m/s) / 26 kg
v1f ≈ -0.8 m/s (south)

So, the final velocity of the cart is approximately -0.8 m/s in the south direction.

To solve this problem, you can use the principle of conservation of momentum.

The momentum of an object is defined as the product of its mass and velocity. In this case, the initial momentum of the system (cart + woman) is the sum of the individual momenta.

The formula for momentum is:

Momentum (p) = mass (m) × velocity (v)

Given:
Mass of the cart (m1) = 26 kg
Mass of the woman (m2) = 52 kg
Initial velocity of the cart (v1) = 1.2 m/s to the south
Initial velocity of the woman (v2) = 0 m/s (at rest)
Final velocity of the woman (v2f) = 1 m/s to the east

Step 1: Calculate the initial momentum of the system (Pi)
Pi = m1 × v1 + m2 × v2

Pi = (26 kg) × (1.2 m/s) + (52 kg) × (0 m/s)
Pi = 31.2 kg·m/s

Step 2: Calculate the final momentum of the system (Pf)
Pf = m1 × (v1f) + m2 × (v2f)

Since the cart is connected to the woman, their final velocity will be the same. Let's assume the final velocity of the cart and the woman is v_final.

Pf = (26 kg) × (v_final) + (52 kg) × (v_final)
Pf = (26 kg + 52 kg) × (v_final)
Pf = 78 kg × (v_final)

Step 3: Equate the initial and final momentum and solve for v_final.
Pi = Pf

31.2 kg·m/s = 78 kg × (v_final)

Divide both sides of the equation by 78 kg
31.2 kg·m/s / 78 kg = v_final

v_final = 0.4 m/s

Therefore, the final velocity of the cart, as well as the woman, is 0.4 m/s to the east.

Using Earth as the frame of reference:

Note: c = cart and p=person/woman

conservation of momentum in y-dir:
m_p * v_py + m_c * v_cy = m_p * v_py' + m_c * v_cy'
note: the first term of left m_p * v_py' is 0 because the person is moving west relative to ground (i.e. no motion in the y-dir). Now, you need to isolate for v_cy'
v_cy' = (m_p * v_py + m_c * v_cy) / m_c
= (52 * 1.2 + 26 * 1.2) / 26
= 3.6 m/s [S] --> the cart is still moves to S but with higher magnitude

conservation of momentum in the x-dir:
m_p * v_px + m_c * v_cx = m_p * v_px' + m_c * v_cx'
Note: all terms on the left side are 0 because the cart and person were moving in the y-dir before (i.e. there is no velocity in x. So, there is no momentum in the x)
0 = m_p * v_px' + m_c * v_cx'
isolate for v_cx'
v_cx' = (m_p * v_px') / m_c
= (52 * 1) / 26
= 2 m/s [E]

Now recombine the vectors v_cy' and v_cx' in order to find the final velocity of cart after this interaction. *use pythagorean theorem for magnitude and tan for angle*