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3-2.Motion in Plane
medium
A ball of mass $1 \;kg$ is thrown vertically upwards and returns to the ground after $3\; seconds$. Another ball, thrown at $60^{\circ}$ with vertical also stays in air for the same time before it touches the ground. The ratio of the two heights are
A
$1:2$
B
$1:1$
C
$2:1$
D
$1:3$
(NEET-2017)
Solution
$T _{1}=\frac{2 u _{1}}{ g }$
$T _{2}=\frac{2 u _{2} \sin \theta}{ g }$
$T _{1}= T _{2}$
$\Rightarrow \frac{2}{ g } u _{1}=\frac{2 u _{2} \sin \theta}{ g } \Rightarrow u _{1}= u _{2} \sin \theta$
$\text { Height }=\frac{ u ^{2} \sin ^{2} \theta}{2 g } \Rightarrow \frac{ H _{1}}{ H _{2}}=\frac{u_{1}^{2}}{u_{2}^{2} \sin ^{2} \theta}$
$\Rightarrow \frac{ H _{1}}{ H _{2}}=1$
Standard 11
Physics
