Question

during the flight of the cannon ball the magnitude of the vertical component of the cannon balls velocity
a remains the same
b decreases and then increases
c increases and then decreases
d increases during the entire flight

Explanation:

Step1: Analyze vertical motion

In projectile motion (like a cannon - ball's flight), the vertical component of velocity \(v_y\) is affected by gravity. The equation for vertical velocity is \(v_y = v_{0y}-gt\), where \(v_{0y}\) is the initial vertical velocity and \(g = 9.8\ m/s^{2}\) (acceleration due to gravity).

Step2: Consider ascent and descent

• Ascent: As the cannon - ball moves up, \(t\) (time) increases. Since \(v_y = v_{0y}-gt\), \(v_y\) decreases (because \(gt\) is positive and being subtracted from \(v_{0y}\)).
• At the highest point: \(v_y = 0\).
• Descent: After the highest point, the direction of motion is downwards. Now, \(v_y= - v_{0y}+gt\) (taking downwards as positive). So, \(v_y\) (magnitude) increases as \(t\) (time of descent) increases.

Answer:

C. Decreases and then increases