Two stones A and B are projected from the same point- B is thrown 1 second after A is thrown- A is projected with a velocity of 60 m-s at an angle 30- with the horizontal and B is projected with velocity u at an angle of 45- with the horizontal- Find u if both stones hit the ground at the same time- Take g-10 m-s

Time of flight of stone A nbsp; T_A= 2u_Asinθg =2(60)sin30^∘10 =6 seconds For the stones to hit at the same time, time of flight of stone B nbsp;(T_B) shou ...

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Standard XIII

Physics

Time of Flight

Two stones A ...

Question

Two stones $A$ and $B$ are projected from the same point. $B$ is thrown $1$ second after $A$ is thrown. $A$ is projected with a velocity of $60 m / s$ at an angle $30^{\circ}$ with the horizontal and $B$ is projected with velocity $u$ at an angle of $45^{\circ}$ with the horizontal. Find $u$ if both stones hit the ground at the same time. (Take $g = 10 m / s$ )

25 m / s

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25 \sqrt{2} m / s

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25 \sqrt{3} m / s

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\frac{25}{2} m / s

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Solution

The correct option is B $25 \sqrt{2} m / s$
Time of flight of stone $A$
$T_{A} = \frac{2 u_{A} sin θ}{g} = \frac{2 (60) sin 30^{\circ}}{10}$
$= 6$ seconds

For the stones to hit at the same time, time of flight of stone $B$ $(T_{B})$ should be $5$ seconds
$T_{B} = \frac{2 u sin θ_{B}}{g}$
$5 = \frac{2 u sin 45^{\circ}}{10}$
$⟹ u = 25 \sqrt{2} m / s$

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The correct option is B 25√2 m/sTime of flight of stone A TA=2uAsinθg=2(60)sin30∘10 =6 seconds For the stones to hit at the same time, time of flight of stone B (TB) should be 5 seconds TB=2usinθBg 5=2usin45∘10 ⟹u=25√2 m/s