SATHEE: Kinematics 5 Question 12

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 $u$ 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 $u$ 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. $u = (3.75 \hat{i} + 6.25 \hat{j}) m / s, 1 s$

Solution:

Let $t$ be the time after which the stone hits the object and $θ$ be the angle which the velocity vector $u$ makes with horizontal. According to question, we have following three conditions.

Vertical displacement of stone is $1.25 m$ .

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Kinematics 5 Question 12

13. An object A is kept fixed at the point x=3m and y=1.25m on a plank P raised above the ground. At time t=0, the plank starts moving along the +x-direction with an acceleration 1.5m/s2. At

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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