If the speed of the Brahmos missile is 9600 m/sec, what should be the speed of the Triumpf missile (in m/sec) so that it should hit the Brahmos missile at point P?
Understand the Problem
The question is asking us to determine the speed of the Triumpf missile so that it can intercept the Brahmos missile at a certain point in space (point P). We need to analyze the motion of both missiles considering the given parameters such as height, distance, angles, and speeds. Using geometry and physics principles, we can calculate the necessary speed for the Triumpf missile.
Answer
The speed of the Triumpf missile must be equal to the speed of the Brahmos missile, so \( V_T = V_B \).
Answer for screen readers
The speed of the Triumpf missile must be equal to the speed of the Brahmos missile, so ( V_T = V_B ).
Steps to Solve
 Identify the parameters We need to gather all the information given in the problem, including the height of the missiles, the distance between them, the angles, and the speeds of the Brahmos missile. Let's denote:
 Height ( h )
 Distance ( D )
 Angle ( \theta )
 Speed of Brahmos ( V_B )
 Speed of Triumpf ( V_T )

Determine time of flight for Brahmos Calculate the time it takes for the Brahmos missile to reach point P using its speed and the distance it has to travel. Use the formula: $$ T_B = \frac{D}{V_B} $$

Analyze the motion of the Triumpf missile The Triumpf missile has to cover the same distance (D) in the same time (T_B) so it can intercept the Brahmos missile. Therefore, we can set up the equation: $$ D = V_T \cdot T_B $$

Substituting the time of flight Replace ( T_B ) with the expression we found previously: $$ D = V_T \cdot \frac{D}{V_B} $$

Solving for Triumpf missile speed Rearrange the equation to solve for ( V_T ): $$ V_T = V_B $$
This means the speed of the Triumpf missile must equal the speed of the Brahmos missile to intercept it.
The speed of the Triumpf missile must be equal to the speed of the Brahmos missile, so ( V_T = V_B ).
More Information
This result reveals that if both missiles travel at the same speed and start from the right positions, the Triumpf missile will be able to intercept the Brahmos missile at point P.
Tips
 Confusing the time of travel for each missile. Ensure to use the appropriate formula to find the time based on the speed and distance for the Brahmos missile first.
 Neglecting to equate the distances they travel in the same time frame.