Question:
Two boys are standing at ends $A$ and $B$ of a ground where $AB = 200\, m$. The boy at B starts running in a direction perpendicular to $AB$ with a speed of $6\, m \,s^{-1}$? The boy at A starts simultaneously with a velocity of $10 \, m \, s^{-1}$ and catches the other at time t where the time $t$ is
Two boys are standing at ends $A$ and $B$ of a ground where $AB = 200\, m$. The boy at B starts running in a direction perpendicular to $AB$ with a speed of $6\, m \,s^{-1}$? The boy at A starts simultaneously with a velocity of $10 \, m \, s^{-1}$ and catches the other at time t where the time $t$ is
Updated On: May 11, 2024
- 50 s
- 20 s
- 25 s
- 12.5 s
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The two boys meet at $C$ after a time $t$.
Taking horizontal motion of boy at $A$ from $A$ to $C, 200 = (10 \cos \theta)t$
or $t =\frac{200}{10 \cos \theta} = \frac{200}{10\left(\frac{\sqrt{\left(10\right)^{2} -\left(6\right)^{2}}}{10}\right)} $
$= \frac{200}{\sqrt{\left(10\right)^{2} - \left(6\right)^{2}}} = \frac{200}{8} = 25 s$
Taking horizontal motion of boy at $A$ from $A$ to $C, 200 = (10 \cos \theta)t$
or $t =\frac{200}{10 \cos \theta} = \frac{200}{10\left(\frac{\sqrt{\left(10\right)^{2} -\left(6\right)^{2}}}{10}\right)} $
$= \frac{200}{\sqrt{\left(10\right)^{2} - \left(6\right)^{2}}} = \frac{200}{8} = 25 s$
Was this answer helpful?
0
0
Top Questions on Motion in a plane
- The resultant of two vectors \( \vec{A} \) and \( \vec{B} \) is perpendicular to \( \vec{A} \) and its magnitude is half that of \( \vec{B} \). The angle between vectors \( \vec{A} \) and \( \vec{B} \) is ________ .
- JEE Main - 2024
- Physics
- Motion in a plane
- If two vectors \(\vec{A}\) and \(\vec{B}\) having equal magnitude \(R\) are inclined at an angle \(\theta\), then
- JEE Main - 2024
- Physics
- Motion in a plane
- A ball dropped from a bridge hits the surface of the water in 3 𝑠. The height of the bridge, ignoring air resistance, is ___ 𝑚 (rounded off to one decimal place). (Use $𝑔 = 9.8 𝑚𝑠^{−2}$)
- IIT JAM BT - 2024
- Physics
- Motion in a plane
- A bullet is fired from a gun at the speed of 280 ms-1 in the direction 30° above the horizontal. The maximum height attained by the bullet is
(g = 9.8 ms-2, sin 30° = 0.5)- NEET (UG) - 2023
- Physics
- Motion in a plane
Car P is heading east with a speed V and car Q is heading north with a speed \(\sqrt{3}\). What is the velocity of car Q with respect to car P?
- KEAM - 2023
- Physics
- Motion in a plane
View More Questions
Questions Asked in COMEDK UGET exam
- A $2\,kg$ mass lying on a table is displaced in the horizontal direction through $50\,cm$. The work done by the normal reaction will be
- COMEDK UGET - 2015
- work, energy and power
- The numbers of $ {H^+}$ ions present in 1 mL of a solution whose pH is 13
- COMEDK UGET - 2015
- Equilibrium
- A mixture of methylamine and dimethylamine is given to you. The reagents used to separate the components of the mixture are
- $\cot^{-1} (21) + \cot^{-1} (13) + \cot^{-1} (-8) =$
- COMEDK UGET - 2015
- Inverse Trigonometric Functions
- Pick the incorrect statement among those given below.
- COMEDK UGET - 2015
- Chemical bonding and molecular structure
View More Questions
Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration