Question

Two paper screens A and B are separated by distance 100 m. A bullet penetrates A and B, at points P and Q respectively, where Q is 10 cm below P. If bullet is travelling horizontally at the time of hitting A, the velocity of bullet at A is nearly _?

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Answer 1

Answer:

700 m/s

Explanation:

As per the provided information in the given question, we have:

• Two paper screens A and B are separated by a distance 100 m.
• A bullet penetrates A and B, at points P and Q respectively, where Q is 10 cm below P.
• Bullet is travelling horizontally at the time of hitting A,

We've been asked to calculate the velocity of bullet A.

We know, the distance an object fall, h is product of half of the gravity, g and the square of the time taken, t.

$\twoheadrightarrow\quad\sf{h=\dfrac{1}{2}\times g\times{t}^{2}}$

– Now, according to the question, the height of bullet will decrease by 10 cm (0.1 m).

$\twoheadrightarrow\quad\sf{0.1=\dfrac{1}{2}\times g\times {t}^{2}}$

We know, g is 9.8 m/s². So,

$\twoheadrightarrow\quad\sf{0.1=\dfrac{1}{2}\times 9.8\times {t}^{2}}$

Performing multiplication in RHS.

$\twoheadrightarrow\quad\sf{0.1=\dfrac{9.8}{2}\times {t}^{2}}$

Performing division.

$\twoheadrightarrow\quad\sf{0.1=4.9\times {t}^{2}}$

Transposing 4.9 from RHS to LHS. It's arithmetic operator will get change.

$\twoheadrightarrow\quad\sf{\dfrac{0.1}{4.9}={t}^{2}}$

Simplifying.

$\twoheadrightarrow\quad\sf{\dfrac{1}{49}={t}^{2}}$

Transposing square from LHS to RHS.

$\twoheadrightarrow\quad\sf{\sqrt{\dfrac{1}{49}}=t}$ $\\\twoheadrightarrow\quad\sf{t=\dfrac{1}{7}\qquad\qquad\qquad \qquad\quad\left\lgroup\begin{matrix} \sf{{eq} ^{n} \: (1)}\end{matrix}\right\rgroup \]}$

We know,

$\twoheadrightarrow\quad\sf{D=Vt}$

Where,

• D is distance.
• V is velocity.
• t is time.

It is given in the question that distance is 100 m. So,

$\twoheadrightarrow\quad\sf{100=Vt}$

From eqⁿ (1),

$\twoheadrightarrow\quad\sf{100=V\times\dfrac{1}{7}}$

Transposing 7 from RHS to LHS. It's arithmetic operator will get change.

$\twoheadrightarrow\quad\sf{100\times 7=V}$

Performing multiplication.

$\twoheadrightarrow\quad\underline{\boxed{\pmb{V=\frak{700\: m/s}}}}$

❝ Therefore, the velocity of bullet A is 700 m/s. ❞

Answer 2

700 m/s is the answer which i got from doubtnut...

hope its helpful army...

btw myself jin me too army..