Kinematics 5 Question 12
13. An object $A$ is kept fixed at the point $x=3 m$ and $y=1.25 m$ on a plank $P$ raised above the ground. At time $t=0$, the plank starts moving along the $+x$-direction with an acceleration $1.5 m / s^{2}$. At
the same instant, a stone is projected from the origin with a velocity $\mathbf{u}$ as shown. A stationary person on the ground observes the stone hitting the object during its downward motion at an angle of $45^{\circ}$ to the horizontal. All the motions are in $x-y$ plane. Find $\mathbf{u}$ and the time after which the stone hits the object. (Take $g=10 m / s^{2}$ ).
(2000, 10M)
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Answer:
Correct Answer: 13. $\mathbf{u}=(3.75 \hat{\mathbf{i}}+6.25 \hat{\mathbf{j}}) m / s, 1 s$
Solution:
- Let $t$ be the time after which the stone hits the object and $\theta$ be the angle which the velocity vector $\mathbf{u}$ makes with horizontal. According to question, we have following three conditions.
Vertical displacement of stone is $1.25 m$.
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