A ball is thrown at an angle and another ball is thrown at an ang… - Vidyadip

MCQ

A ball is thrown at an angle $\theta $ and another ball is thrown at an angle $(90^o -\theta )$ with the horizontal from the same point with same speed $40\,ms^{-1}$. The second ball reaches $50\,m$ higher than the first ball. Find their individual heights?

✓
$15\,m,\,65\,m$
B
$25\,m,\,75\,m$
C
$10\,m,\,60\,m$
D
$20\,m,\,70\,m$

✓

Answer

Correct option: A.

$15\,m,\,65\,m$

a
$\frac{\mathrm{H}_{1}}{\mathrm{H}_{2}}=\tan ^{2} \theta$

$\mathrm{H}_{2}-\mathrm{H}_{1}=50$

$\mathrm{H}_{2}\left(1-\tan ^{2} \theta\right)=50$

$\Rightarrow \frac{\mathrm{u}^{2} \cos ^{2} \theta}{2 \mathrm{g}} \times\left(\frac{\cos ^{2} \theta-\sin ^{2} \theta}{\cos ^{2} \theta}\right)=50$

$\Rightarrow 1-2 \sin ^{2} \theta=\frac{5}{8}$

$\Rightarrow \sin ^{2} \theta=\frac{3}{16}$

so $\mathrm{H}_{1}=\frac{\mathrm{u}^{2} \sin ^{2} \theta}{2 \mathrm{g}}=\frac{(40)^{2}}{2 \times 10} \times \frac{3}{16}=15 \mathrm{m}$

so $\mathrm{H}_{2}=65 \mathrm{m}$

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