NTA Abhyas 2020
- Exam
- NTA Abhyas
- Year
- 2020
- Subject
- Physics
- Chapter
- Motion in Two Dimensions
NTA Abhyas 2020 · Physics · Motion in Two Dimensions
If a stone is& to hit at a point which is at a distance d away and...
If a stone is& to hit at a point which is at a distance away and at a height above the point from where the stone starts, then what is the value of initial speed , if the stone is launched at an angle
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Options
- A\dfrac{g}{\text\cos\theta}\sqrt{\dfrac{d}{2\left(d \text\tan\theta - h\right)}}
- B\dfrac{d}{\text\cos\theta}\sqrt{\dfrac{g}{2\left(d \text\tan\theta - h\right)}}
- C
- D\sqrt{gd^{2}\left(d - h\right)}
Correct answer
B. \dfrac{d}{\text\cos\theta}\sqrt{\dfrac{g}{2\left(d \text\tan\theta - h\right)}}
Step-by-step solution
Using equation of motion for projectile in x and y-direction.
\text{h} = \left(u \text\sin\theta\right)t - \dfrac{1}{2}gt^{2}
d = \left(\text{u}\text\cos\theta\right)t or t = \dfrac{d}{\text{u}\text\cos\theta}
⟹ h = u \text\sin\theta\text{.}\dfrac{d}{u \text\cos\theta} - \dfrac{1}{2}\text{g}\text{.}\dfrac{\text{d}2}{u^{2}\cos^{2}\theta}
⟹ \text{u} = \dfrac{d}{\text\cos\theta}\sqrt{\dfrac{g}{2\left(\text{d}\text{t}an\theta - h\right)}}
\text{h} = \left(u \text\sin\theta\right)t - \dfrac{1}{2}gt^{2}
d = \left(\text{u}\text\cos\theta\right)t or t = \dfrac{d}{\text{u}\text\cos\theta}
⟹ h = u \text\sin\theta\text{.}\dfrac{d}{u \text\cos\theta} - \dfrac{1}{2}\text{g}\text{.}\dfrac{\text{d}2}{u^{2}\cos^{2}\theta}
⟹ \text{u} = \dfrac{d}{\text\cos\theta}\sqrt{\dfrac{g}{2\left(\text{d}\text{t}an\theta - h\right)}}