Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
Trajectories of two projectiles are shown in figure. Let\[{{T}_{1}}\]and\[{{T}_{2}}\]be the time periods and\[{{u}_{1}}\] and\[{{u}_{2}}\]their speeds of projection. Then
(1) \[{{T}_{2}}>{{T}_{1}}\] (2) \[{{T}_{1}}={{T}_{2}}\] (3) \[{{u}_{1}}>{{u}_{2}}\] (4) \[{{u}_{1}}<{{u}_{2}}\]
A) 1, 2 and 3 are correct.
B) 1 and 2 are correct.
C) 2 and 4 are correct.
D) 1 and 3 are correct.
Correct Answer: C
Solution :
Maximum height and time of flight depend on the vertical component of initial velocity \[{{H}_{1}}={{H}_{2}}\] \[\Rightarrow \] \[{{u}_{{{y}_{1}}}}={{u}_{{{y}_{2}}}}\] Here, \[R=\frac{{{u}^{2}}\sin 2\theta }{g}=\frac{2(u\sin \theta )(u\cos \theta )}{g}\] \[=\frac{2{{u}_{x}}{{u}_{y}}}{g}\] \[{{R}_{2}}>{{R}_{1}}\] \[\therefore \] \[{{u}_{{{x}_{2}}}}>{{u}_{{{x}_{1}}}}\]or\[{{u}_{2}}>{{u}_{1}}\]
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