Answer
Verified
376.5k+ views
Hint: In order to solve this question, we are first going to look for the figure and write all the information given the velocities, distance and the acceleration. Then, the relative motion is assessed and the relative acceleration and the velocities are calculated after which the minimum distance is calculated.
Formula used:
The minimum distance is given by the formula
\[{d_{\min }} = d\cos \theta \]
Where, \[d\]is the distance between the projectiles and \[\theta \]is the angle difference between them.
Complete answer:
Let us see the figure as given in the question, we see that the velocities of the two projectiles are
$ {v_1} = 20\sqrt 3 m{s^{ - 1}} \\
{v_2} = 20m{s^{ - 1}} \\ $
The velocity of the projectiles with respect to the horizontal axes are:
$ {v_{1x}} = - 10\sqrt 3 m{s^{ - 1}} \\
{v_{2y}} = 10\sqrt 3 m{s^{ - 1}} \\ $
The distance between the two projectiles at the time of firing is
\[d = 20\sqrt 3 m\]
The acceleration of the two projectiles are
$ {a_1} = g \\
{a_2} = g \\ $
Thus, the relative acceleration of the two projectiles is
\[{a_{12}} = 0\]
Thus we see that the relative motion of the projectiles is uniform.
The relative velocity of the two projectiles can be calculated as
\[{v_{21}} = \sqrt {{{\left( {20} \right)}^2} + {{\left( {20\sqrt 3 } \right)}^2}} \]
Now, the minimum distance is given by the formula
\[{d_{\min }} = d\cos {60^ \circ }\]
Putting the value of the initial distance between the projectiles, we get
\[{d_{\min }} = 20\sqrt 3 \times \dfrac{1}{2} = 10\sqrt 3 \,m\]
Note: Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile, and its path is called its trajectory. The two projectiles fired simultaneously have the zero relative acceleration which makes it the uniform relative motion.
Formula used:
The minimum distance is given by the formula
\[{d_{\min }} = d\cos \theta \]
Where, \[d\]is the distance between the projectiles and \[\theta \]is the angle difference between them.
Complete answer:
Let us see the figure as given in the question, we see that the velocities of the two projectiles are
$ {v_1} = 20\sqrt 3 m{s^{ - 1}} \\
{v_2} = 20m{s^{ - 1}} \\ $
The velocity of the projectiles with respect to the horizontal axes are:
$ {v_{1x}} = - 10\sqrt 3 m{s^{ - 1}} \\
{v_{2y}} = 10\sqrt 3 m{s^{ - 1}} \\ $
The distance between the two projectiles at the time of firing is
\[d = 20\sqrt 3 m\]
The acceleration of the two projectiles are
$ {a_1} = g \\
{a_2} = g \\ $
Thus, the relative acceleration of the two projectiles is
\[{a_{12}} = 0\]
Thus we see that the relative motion of the projectiles is uniform.
The relative velocity of the two projectiles can be calculated as
\[{v_{21}} = \sqrt {{{\left( {20} \right)}^2} + {{\left( {20\sqrt 3 } \right)}^2}} \]
Now, the minimum distance is given by the formula
\[{d_{\min }} = d\cos {60^ \circ }\]
Putting the value of the initial distance between the projectiles, we get
\[{d_{\min }} = 20\sqrt 3 \times \dfrac{1}{2} = 10\sqrt 3 \,m\]
Note: Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile, and its path is called its trajectory. The two projectiles fired simultaneously have the zero relative acceleration which makes it the uniform relative motion.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE