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Using $\vec{s} = \vec{r}_0 + \vec{u}t + \frac{1}{2}\vec{a}t^2$:
- $x = 2 + 5(2) + \frac{1}{2}(4)(2^2) = 2 + 10 + 8 = 20$
- $y = 4 + 4(2) + \frac{1}{2}(4)(2^2) = 4 + 8 + 8 = 20$
- Distance from origin $D = \sqrt{20^2 + 20^2} = 20\sqrt{2}\text{ m}$.
Persistent Occiput Posterior (POP) position is a common cause of prolonged second stage and arrest of descent. In OP position:
- The fetal head presents with a larger diameter to the pelvis: occipito-frontal diameter \(\approx 11.5\,\text{cm}\) vs. sub-occipito-bregmatic \(9.5\,\text{cm}\) in OA
- Internal rotation from OP to OA requires \(135Β°\) rotation (vs. \(90Β°\) from OT, \(45Β°\) from OA)
- Causes: anthropoid/android pelvis, deflexed head
Management options:
- Manual rotation to OA (Barton's maneuver)
- Expectant management if maternal/fetal condition good
- Instrumental delivery: forceps (Kielland's rotational forceps) or rotational vacuum
- Cesarean section if rotation fails or fetal distress
CPD is less likely in a multigravida who delivered previously without CPD. Hypotonic labor would show weak contractions on partograph/CTG.
A projectile is launched from the ground with initial velocity $\vec{u} = u_0\hat{i} + v_0\hat{j}$. Gravity acts in the $-y$ direction. The maximum displacement in the $x$-direction is:
Time of flight $= \dfrac{2v_0}{g}$ (time for vertical displacement to return to zero).
Horizontal range $= u_0 \times \dfrac{2v_0}{g} = \mathbf{\dfrac{2u_0 v_0}{g}}$
If North is at the bottom of the page, then all compass directions are inverted:
- North β bottom
- South β top
- East β left
- West β right
South-East in real terms = top + left on this rotated page = Top-left.
This type of question tests your ability to mentally rotate a reference frame β a critical skill in architectural plan reading.
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