A projectile is projected with the velocity of (3 i +4 j ) m / s ....

A projectile is projected with the velocity of

(3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}

. The horizontal range of the projectile will be A projectile is projected with the velocity of (3 i +4 j ) m / s . The horizontal range of the projectile will be

A projectile is projected with the velocity of (3 i +4 j ) m / s . The horizontal range of the projectile will be

Options

A $1.2 \mathrm{ m}$
B $2.4 \mathrm{ m}$
C $3.6 \mathrm{ m}$
D $4.5 \mathrm{ m}$

Correct answer

B. $2.4 \mathrm{ m}$

Step-by-step solution

Given,

\mathbf{v}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}} \therefore \quad v=|\mathrm{v}|=\sqrt{3^2+4^2} \Rightarrow

v=5

\mathrm{ m}

\mathrm{s}

From figure,

<img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fpyq%252Fbitsat%252FS68DyZBu4WVIyvgm-kVZTbqOsJd6ueHWTqIkKHSEDW4.original.fullsize.png%3Falt%3Dmedia \text{ and } clean=1 \text{ and } v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fbitsat%2FS68DyZBu4WVIyvgm-kVZTbqOsJd6ueHWTqIkKHSEDW4.original.fullsize.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fbitsat%2FS68DyZBu4WVIyvgm-kVZTbqOsJd6ueHWTqIkKHSEDW4.original.fullsize.png?alt=media"> \\ \sin \theta=\frac{4}{5}

and

\cos \theta=\frac{3}{5}\because \quad R=\frac{v^2 \sin 2 \theta}{g}=\frac{v^2 \cdot 2 \sin \theta \cdot \cos \theta}{g}=\frac{5 \times 5 \times 2 \times \frac{4}{5} \times \frac{3}{5}}{10}=24 \mathrm{ m}

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