Question

A bullet is fired straight up from a gun with a

muzzle velocity of 282 m/s.
Neglecting
air resistance, what will be its
displacement after 4.4 s? The acceleration of
gravity is 9.8 m/s².
Answer in units of m.

Answer 1

To find the displacement of the bullet after 4.4 seconds when fired straight up with a muzzle velocity of 282 m/s, you can use the following kinematic equation:

\[ \text{Displacement} = \text{Initial Velocity} × \text{Time} - \frac{1}{2} × \text{Acceleration due to Gravity} × \text{Time}^2 \]

Given:

Initial velocity (\(v_0\)) = 282 m/s (upward)

Time (\(t\)) = 4.4 s

Acceleration due to gravity (\(g\)) = 9.8 m/s² (downward)

Plug these values into the equation:

\[ \text{Displacement} = 282 m/s × 4.4 s - \frac{1}{2} × 9.8 m/s² × (4.4 s)^2 \]

Now, calculate the displacement:

\[ \text{Displacement} = 1239.2 m - 96.664 m \]

Subtract 96.664 m from 1239.2 m to find the displacement:

\[ \text{Displacement} = 1142.536 m \]

So, the displacement of the bullet after 4.4 seconds, neglecting air resistance, is approximately 1142.536 meters upward from its initial position.