Problem 98 - Algebra and Trigonometry Real Mathematics, Real People

Question

A gun with a muzzle velocity of 1200 feet per second is fired at an angle of \(6^{\circ}\) above the horizontal. Find the vertical and horizontal components of the velocity.

Step-by-Step Solution

Answer

The horizontal component of the velocity is about \(1196.2\) feet/sec, and the vertical component of the velocity is about \(125.6\) feet/sec.

Step 1: Identify given variables

The muzzle velocity \(v = 1200\) feet/sec and the angle \(\theta = 6^{\circ}\) is given.

Step 2: Find the horizontal component of the velocity

The horizontal component of the velocity (represented as \(v_x\)) can be found using the formula \(v_x = v \cos(\theta)\), where \(v\) is the muzzle velocity and \(\theta\) is the angle. Plugging the given values into this formula gives \(v_x = 1200 \cos(6^{\circ})\).

Step 3: Find the vertical component of the velocity

The vertical component of the velocity (represented as \(v_y\)) can be found using the formula \(v_y = v \sin(\theta)\), where \(v\) is the muzzle velocity and \(\theta\) is the angle. Plugging the given values into this formula gives \(v_y = 1200 \sin(6^{\circ})\).