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Question

Physics Question on Motion in a plane

A stone is thrown at 25m/s25 \, \text{m} / \text{s} at 53o53^{o} above the horizontal. At what time its velocity is at 45o45^{o} below the horizontal?

A

0.5s0.5 \, \, \text{s}

B

4s4 \, \, \text{s}

C

3.5s3.5 \, \, \text{s}

D

2.5s2.5 \, \, \text{s}

Answer

3.5s3.5 \, \, \text{s}

Explanation

Solution

Horizontal component of velocity, throughout the motion remain constant using ucosθ=vcosαucos \, \theta =vcos \, \alpha 25cos53=vcos?4525cos 53 ^\circ = v cos ? 45 ^\circ v=25×35.2\Longrightarrow v=25\times \frac{3}{5}.\sqrt{2} =152=15\sqrt{2} vy=vsin45=15\Longrightarrow v_{y}=vsin 45 = 15 Now using Vy=uy+aytiny \, \, \, V_{y}=u_{y}+a_{y}t \, in \, \, y- direction, 15=25sin53?-15=25sin 53? 15=25×4510t-15=25\times \frac{4}{5}-10 \, t t=3.5sec\Longrightarrow t=3.5 \, \text{sec}