First slide

Projection Under uniform Acceleration

Question

A body is projected up along a smooth inclined plane with velocity u from the point A as shown in Fig.. The angle of inclination is 45° and the top is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of u? The length of inclined plane is $20 \sqrt{2}$ m.

Difficult

A

40 ms^-1
B

$40 \sqrt{2} {ms}^{- 1}$
C

20 ms-1
D

$20 \sqrt{2} {ms}^{- 1}$

Solution

Angle of projection from B is 45°. As the body is able to cross the well of diameter 40 m, hence
$R = \frac{v^{2}}{g} or v = \sqrt{gR} = \sqrt{10 \times 40} = 20 {ms}^{- 1} On the inclined plane, the retardation is gsinα = gsin 45 ° = 10 / \sqrt{2} {ms}^{- 2} {Usingv}^{2} - u^{2} = 2 ax (20)^{2} - u^{2} = 2 \times (- \frac{10}{\sqrt{2}}) \times 20 \sqrt{2} u = 20 \sqrt{2} {ms}^{- 1}$

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