362022
A body is projected in such a way that its horizontal range and time of flight both are equal to \(\frac{{\sqrt 3 }}{g}\) in numerical values. The angle of projection will be:-
362025
A projectile can have the same range \(R\) for two angles of projection. If \({t_1}\) and \({t_2}\) be the times of flight in the two cases, then what is the product of two times of flight?
1 \({t_1}{t_2}\alpha {R^2}\)
2 \({t_1}{t_2}\alpha R\)
3 \({t_1}{t_2}\alpha \frac{1}{R}\)
4 \({t_1}{t_2}\alpha \frac{1}{{{R^2}}}\)
Explanation:
The horizontal range is the same for the angles of projection \(\theta \) and \((90^\circ - \theta )\) \({t_1} = \frac{{2u\sin \theta }}{g}\) \({t_2} = \frac{{2u\sin (90^\circ - \theta )}}{g} = \frac{{2u\cos \theta }}{g}\) \({t_1}{t_2} = \frac{{2u\sin \theta }}{g} \times \frac{{2u\cos \theta }}{g} = \frac{2}{g}\left[ {\frac{{{u^2}\sin \theta }}{g}} \right] = \frac{2}{g}R\) where \(R = \frac{{{u^2}\sin 2\theta }}{g}\) Hence \({t_1}{t_2}\alpha R\) (as \(R\) is constant)
362022
A body is projected in such a way that its horizontal range and time of flight both are equal to \(\frac{{\sqrt 3 }}{g}\) in numerical values. The angle of projection will be:-
362025
A projectile can have the same range \(R\) for two angles of projection. If \({t_1}\) and \({t_2}\) be the times of flight in the two cases, then what is the product of two times of flight?
1 \({t_1}{t_2}\alpha {R^2}\)
2 \({t_1}{t_2}\alpha R\)
3 \({t_1}{t_2}\alpha \frac{1}{R}\)
4 \({t_1}{t_2}\alpha \frac{1}{{{R^2}}}\)
Explanation:
The horizontal range is the same for the angles of projection \(\theta \) and \((90^\circ - \theta )\) \({t_1} = \frac{{2u\sin \theta }}{g}\) \({t_2} = \frac{{2u\sin (90^\circ - \theta )}}{g} = \frac{{2u\cos \theta }}{g}\) \({t_1}{t_2} = \frac{{2u\sin \theta }}{g} \times \frac{{2u\cos \theta }}{g} = \frac{2}{g}\left[ {\frac{{{u^2}\sin \theta }}{g}} \right] = \frac{2}{g}R\) where \(R = \frac{{{u^2}\sin 2\theta }}{g}\) Hence \({t_1}{t_2}\alpha R\) (as \(R\) is constant)
362022
A body is projected in such a way that its horizontal range and time of flight both are equal to \(\frac{{\sqrt 3 }}{g}\) in numerical values. The angle of projection will be:-
362025
A projectile can have the same range \(R\) for two angles of projection. If \({t_1}\) and \({t_2}\) be the times of flight in the two cases, then what is the product of two times of flight?
1 \({t_1}{t_2}\alpha {R^2}\)
2 \({t_1}{t_2}\alpha R\)
3 \({t_1}{t_2}\alpha \frac{1}{R}\)
4 \({t_1}{t_2}\alpha \frac{1}{{{R^2}}}\)
Explanation:
The horizontal range is the same for the angles of projection \(\theta \) and \((90^\circ - \theta )\) \({t_1} = \frac{{2u\sin \theta }}{g}\) \({t_2} = \frac{{2u\sin (90^\circ - \theta )}}{g} = \frac{{2u\cos \theta }}{g}\) \({t_1}{t_2} = \frac{{2u\sin \theta }}{g} \times \frac{{2u\cos \theta }}{g} = \frac{2}{g}\left[ {\frac{{{u^2}\sin \theta }}{g}} \right] = \frac{2}{g}R\) where \(R = \frac{{{u^2}\sin 2\theta }}{g}\) Hence \({t_1}{t_2}\alpha R\) (as \(R\) is constant)
NEET Test Series from KOTA - 10 Papers In MS WORD
WhatsApp Here
PHXI04:MOTION IN A PLANE
362022
A body is projected in such a way that its horizontal range and time of flight both are equal to \(\frac{{\sqrt 3 }}{g}\) in numerical values. The angle of projection will be:-
362025
A projectile can have the same range \(R\) for two angles of projection. If \({t_1}\) and \({t_2}\) be the times of flight in the two cases, then what is the product of two times of flight?
1 \({t_1}{t_2}\alpha {R^2}\)
2 \({t_1}{t_2}\alpha R\)
3 \({t_1}{t_2}\alpha \frac{1}{R}\)
4 \({t_1}{t_2}\alpha \frac{1}{{{R^2}}}\)
Explanation:
The horizontal range is the same for the angles of projection \(\theta \) and \((90^\circ - \theta )\) \({t_1} = \frac{{2u\sin \theta }}{g}\) \({t_2} = \frac{{2u\sin (90^\circ - \theta )}}{g} = \frac{{2u\cos \theta }}{g}\) \({t_1}{t_2} = \frac{{2u\sin \theta }}{g} \times \frac{{2u\cos \theta }}{g} = \frac{2}{g}\left[ {\frac{{{u^2}\sin \theta }}{g}} \right] = \frac{2}{g}R\) where \(R = \frac{{{u^2}\sin 2\theta }}{g}\) Hence \({t_1}{t_2}\alpha R\) (as \(R\) is constant)
