Answer

Verified

342k+ views

**Hint:**We shall analyze the motion of the bullets due to their vertical acceleration due to gravity. Since the bullets have a horizontal component of velocity, therefore they will not be falling freely in a straight-line path due to action of gravity. Thus, we will apply equations of motion in the vertical motion to find the time taken.

**Complete answer:**

a).Initially, the bullets have only a horizontal component of velocity and the vertical component of velocity is zero. However, the bullets have an acceleration in the downward direction which makes their path semi-parabolic. Thus, both the bullets will strike the ground due to their acceleration due to gravity in the vertically downward direction.

b).Time taken in for the bullets to reach the ground is given by Newton’s second equation of motion. The equation is:

$s=ut+\dfrac{1}{2}a{{t}^{2}}$

Where,

$s=$ displacement of body

$u=$ initial velocity of body

$t=$ time taken

$a=$ acceleration of the body

We shall apply this equation for the vertical motion of the bullets only. The vertical component of initial velocity is zero for both the bullets. Thus, $u=0$. The vertical acceleration acting on the bullets is the acceleration due to gravity. Thus, $a=g$. The vertical height from which the bullets are being fired is $19.6m$. Thus, $s=19.6m$.

Thus, we get the equation as:

$19.6=\left( 0 \right)t+\dfrac{1}{2}g{{t}^{2}}$

$\Rightarrow 19.6=\dfrac{1}{2}g{{t}^{2}}$

Given that $g=9.8m{{s}^{-2}}$,

$\Rightarrow 19.6=\dfrac{1}{2}\left( 9.8 \right){{t}^{2}}$

$\Rightarrow {{t}^{2}}=\dfrac{19.6\left( 2 \right)}{9.8}$

$\Rightarrow {{t}^{2}}=4$

$\begin{align}

& \Rightarrow t=\sqrt{4} \\

& \Rightarrow t=\pm 4 \\

\end{align}$

Ignoring the negative value because time is always positive.

Therefore, both the bullets will strike the ground at the same time, that is, $2$seconds. This is because the time taken is independent of initial velocities of bullets.

c).The path followed by the bullets will be a semi-parabolic path with different range due to different horizontal velocities.

**Note:**

Here, we see that the time taken by the bullets to strike the ground is independent of the velocity of the bullet. It is only dependent on the vertical and acceleration which is the same for both the bullets. Hence, both bullets will strike the ground at the same time.

Recently Updated Pages

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

Basicity of sulphurous acid and sulphuric acid are

The branch of science which deals with nature and natural class 10 physics CBSE

What is the stopping potential when the metal with class 12 physics JEE_Main

The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Why is the adrenaline hormone called fight or flight class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between lanthanoids and actinoids class 12 chemistry CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Give 10 examples of unisexual and bisexual flowers

Open circulatory system is present in I Arthropods class 12 biology CBSE

Name the highest peak of the Indian Himalayas class 8 social science CBSE