A bullet is fired straight up from a gun with a
muzzle velocity of 170 m/s.
Neglecting air resistance, what will be its
displacement after 5.8 s? The acceleration of
gravity is 9.8 m/s2 .
Answer in units of m.
To find the displacement of the bullet after 5.8 seconds, we can use the kinematic equation:
displacement = initial velocity × time + 0.5 × acceleration × time²
Given:
Initial velocity (u) = 170 m/s (muzzle velocity of the bullet)
Time (t) = 5.8 s
Acceleration (a) = -9.8 m/s² (taking gravity into account)
Plugging in the values, we get:
displacement = (170 m/s) × (5.8 s) + 0.5 × (-9.8 m/s²) × (5.8 s)²
Simplifying the equation gives:
displacement = 170 m/s × 5.8 s - 0.5 × 9.8 m/s² × 33.64 s²
displacement = 986 m - 1653.98 m
displacement ≈ -667.98 m
The negative sign indicates that the displacement is in the opposite direction to the initial motion (upward direction), which means that after 5.8 seconds, the bullet will be 667.98 meters below its starting point.