Shortcut Methods and Tricks to Solve Numerical Problems Related to Impact and Collision:

JEE Main Level

• For vertical motion problems, use the equation of motion: $$h_{max}=v_i^2/2g$$ where $$h_{max}$$ is the maximum height, $$v_i$$ is the initial velocity, and $$g$$ is the acceleration due to gravity.

• For collisions in one dimension, use the conservation of momentum: $$m_1{v}_1+m_2{v}_2=m_1{u}_1+m_2{u}_2$$ where $$m_1$$ and $$m_2$$ are the masses of the two objects, $$v_1$$ and $$v_2$$ are their initial velocities, and $$u_1$$ and $$u_2$$ are their final velocities.

• For collisions in two dimensions, use the conservation of momentum in both the $$x$$ and $$y$$ directions. Also, consider the energy balance equation $$E_i=E_f$$ or $$K_i=K_f$$ in the case of elastic collision.

CBSE Board Level

• Use the same formulas and principles as for the JEE Main level, but the problems may be simpler and involve smaller values.

Typical Questions

• To find the height reached by a ball thrown vertically upwards, use the formula: $$h_{max}=v_i^2/2g$$

• To find the velocity of a ball after collision with another ball at rest, use the conservation of momentum: $$v_{2f}=(2m_1{v}_1)/(m_1+m_2)$$

• To find the velocity of a car after collision with a truck at rest, use the conservation of momentum: $$v_{1f}=\frac{M-2m}{M+m}{v}_1$$

Additional Tips

• Draw diagrams to visualize the problem. This can help you to identify the forces involved and the directions of motion.

• Break down the problem into smaller steps. This can make it easier to find a solution.

• Be careful with units. Make sure to use consistent units throughout the problem.

• Don’t forget to check your answer. This is especially important for more complex problems.