Category: HC Verma Part 1: Mechanics

Problem Statement Solve the momentum/collision problem: A car A is 100 m behind car B. Both move at 72 km/h. Car B decelerates at 1 m/s². Find the minimum deceleration that A must apply to avoid collision. Relative motion: in the reference frame of B, A approaches at relative velocity 0 but if B decelerates,…

Problem Statement A swimmer can swim at 5 m/s in still water. A river flows at 3 m/s. In what direction should the swimmer head to go directly across? Find the effective crossing speed. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the…

Problem Statement Rain falls vertically at 10 m/s. A man walks north at 6 m/s. Find the direction in which the man should hold his umbrella. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant…

Problem Statement Solve the kinematics problem: Particle A has velocity $10\hat{i}$ m/s and particle B has velocity $10\hat{j}$ m/s. Find the velocity of A relative to B. $\vec{v}_{AB} = \vec{v}_A – \vec{v}_B$ Step 1: $\vec{v}_{AB} = 10\hat{i} – 10\hat{j}$ m/s. Step 2: $|\vec{v}_{AB}| = \sqrt{100+100} = 10\sqrt{2} \approx 14.1$ m/s at 45° below t Given…

Problem Statement Solve the kinematics problem: A projectile is launched at speed $u$ and angle $\theta$. At what time does the speed equal $u\cos\theta$? At the highest point, $v_y = 0$ and $v = v_x = u\cos\theta$ Step 1: The speed equals $u\cos\theta$ when $v_y = 0$, i.e., at the highest point. Step 2: Time…

Problem Statement A gun fires a bullet at a monkey sitting in a tree. The monkey lets go of the branch and falls freely the instant it sees the flash. Show that the bullet always hits the monkey (ignoring air resistance). Given Information See problem statement for all given quantities. Physical Concepts & Formulas This…

Problem Statement Solve the kinematics problem: A particle moves such that its position vector is $\vec{r} = (3\cos\omega t)\hat{i} + (3\sin\omega t)\hat{j}$ m. Find the speed. $\vec{v} = d\vec{r}/dt$; speed = $|\vec{v}|$ Step 1: $\vec{v} = -3\omega\sin\omega t\,\hat{i} + 3\omega\cos\omega t\,\hat{j}$. Step 2: $|\vec{v}| = 3\omega\sqrt{\sin^2\ome Given Information See problem statement for all given quantities.…

Problem Statement A wheel starts from rest and has an angular acceleration of 5 rad/s². Find the angle turned in 4 s and the angular velocity at that time. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires…

Problem Statement Solve the rotational mechanics problem: A wheel of radius 0.4 m rotates so that a point on the rim has a linear speed of 8 m/s. Find the angular velocity. $v = r\omega \Rightarrow \omega = v/r$ Step 1: $\omega = v/r = 8/0.4 = 20$ rad/s. $$\boxed{\omega = 20\text{ rad/s}}$$ Given Information…

Problem Statement Solve the Newton’s Laws / mechanics problem: A particle moves along a circle of radius 1 m. Its speed increases at a rate of 3 m/s². When its speed is 4 m/s, find the total acceleration. $a_t = dv/dt$ (tangential); $a_c = v^2/r$ (centripetal); $a = \sqrt{a_t^2 + a_c^2}$ Step 1: $a_t =…