List of top Physics Questions on Motion in a plane

The equation of path of a projectile moving in x-y plane is given by $ y = x - \frac{x^2}{25} $, then the initial speed and maximum height of particle will be (take $ g = 10 \, \text{m/s}^2 $):
A flag on a boat at rest is fluttering in the south-east direction when the wind is blowing at a speed of \(72\) kmph. If the boat starts moving towards south with a speed of \(36\sqrt2\) kmph, then the direction of the flag on the boat is:
If a body is projected from the ground at an angle of $45^\circ$ with the horizontal, then the ratio of the velocities of the body at maximum height and at half of the maximum height is:
A body is projected from a point which is at a height of \(5\) m from the ground with a velocity of \(28\ \mathrm{ms^{-1}}\) at an angle of \(30^\circ\) above the horizontal. The horizontal distance travelled by the body when it reaches a point which is at a height of \(2\) m from the ground is \[ (g=10\ \mathrm{ms^{-2}}) \]
Two bodies A and B separated by some distance on the ground are projected simultaneously in opposite directions towards each other. Body B is projected with a velocity of $20\,ms^{-1}$ at an angle of $45^\circ$ with the horizontal and body A is projected at an angle of $30^\circ$ with the horizontal. If the two bodies collide at a time of $\sqrt{2}\,s$ from the beginning of their motion, then the initial distance between the bodies A and B is nearly}
The position vector of a particle is \(\overset{⃗}{r} = acosωt\hat{i}+asinωt\hat{j}\). Calculate the angle between its position vector and the velocity vector.
(\(cos0 = 1,cos90 = 0,cos60 = 0.5,sin30 = 0.5,sin0 = 0\))
The magnitudes of three vectors \(\vec A,\vec B,\vec C\) are \(12,5\), and \(13\) units respectively and \(\vec A+\vec B=\vec C\). The angle between \(\vec A\) and \(\vec B\) is
The ratio between maximum and minimum values of two vectors \(\vec A\) and \(\vec B\), where \(A>B\), is \(4:1\). Then the ratio between the magnitudes of two vectors is
An aeroplane is moving in a circular path with a speed of \(450\ \text{kmph}\). What is the change in velocity in half revolution?
If \(|\vec A+\vec B|=|\vec A-\vec B|\), then the angle between the two vectors \(\vec A\) and \(\vec B\) is
A particle moves along a parabolic path $y = 9x^2$ in such a way that the x-component of velocity remains constant. If the total acceleration of the particle is $2\hat{j}\text{ m s}^{-2}$, find the x-component of velocity.
The vertical displacement (y in metre) of a projectile in terms of its horizontal displacement (x in metre) is given by $y=(\sqrt{3}x - 0.2x^2)$. The time of flight of the projectile is (Acceleration due to gravity = 10 ms$^{-2}$)
If a body projected with a velocity of 19.6 ms⁻¹ reaches a maximum height of 9.8 m, then the range of the projectile is (Neglect air resistance)
A cannon on a cliff 55 m above the ground fires a shell with a velocity of \(50\hat{i}+50\hat{j}\) ms\textsuperscript{−1}. The displacement vector of the shell when it hits the ground is (Acceleration due to gravity = 10 ms\textsuperscript{−2})
Two vectors are given by $\vec{A} = \hat{i} - 2\hat{j} + 3\hat{k}$ and $\vec{B} = 2\hat{i} - 4\hat{j} + 3\hat{k}$. The unit vector along $\vec{A} + \vec{B}$ is
A ball projected at an angle of 45$^\circ$ with the horizontal crosses two points at equal heights separated by a distance at times 2 s and 8 s respectively. The horizontal distance between the two points is (Acceleration due to gravity = 10 ms$^{-2}$)
The minimum velocity of a projectile is 50% of its maximum velocity. If the minimum velocity of the projectile is $10~\text{m s}^{-1}$ then the time of flight of the projectile is (Acceleration due to gravity = $10~\text{m s}^{-2}$
If the velocity (in \( \text{m s}^{-1} \)) of a particle at any instant \( t \) is given by \( 2.0\hat{i} + 3.0t\hat{j} \), then the magnitude of its acceleration (in \( \text{m s}^{-2} \)) is
The area of rectangle with sides as \(\vec A=3\hat i+4\hat j\) and \(\vec B=\hat i+3\hat j\) is
If \(A+B=C\) and \(A^2+B^2=C^2\), then the angle between vectors \(A\) and \(B\) is
The area of rectangle with sides as \(\vec A=3\hat i+4\hat j\) and \(\vec B=\hat i+3\hat j\) is
If \(A+B=C\) and \(A^2+B^2=C^2\), then the angle between vectors \(A\) and \(B\) is
A ball is thrown vertically upwards with an initial velocity of $ 20 \, \text{m/s} $. How high will the ball rise? (Take $ g = 10 \, \text{m/s}^2 $)
A person travelling on a straight line moves with a uniform velocity \( v_1 \) for a distance \( x \) and with a uniform velocity \( v_2 \) for the next \( \frac{3x}{2} \) distance. The average velocity in this motion is \( \frac{50}{7} \, \text{m/s} \). If \( v_1 \) is 5 m/s, then \( v_2 \) is ___ m/s.
The speed \( v \) of a wave on a string depends on the tension \( F \) in the string and the mass per unit length \( m/L \) of the string. If it is known that [F] = [ML][T]–2, the values of the constants \( a \) and \( b \) in the following equation for the speed of a wave on a string are: \[ v = (\text{constant}) F^a \left( \frac{m}{L} \right)^b \]