A bullet is fired straight up from a gun with a
muzzle velocity of 214 m/s.
Neglecting air resistance, what will be its
displacement after 8.2 s? The acceleration of
gravity is 9.8 m/s2 .
Answer in units of m
To find the displacement of the bullet after 8.2 seconds, we can use the equation of motion:
s = ut + (1/2)at^2
Where:
s = displacement
u = initial velocity
a = acceleration
t = time
Given:
u = 214 m/s (muzzle velocity)
a = -9.8 m/s^2 (acceleration due to gravity, negative because it acts in the opposite direction of the bullet's motion)
t = 8.2 s (time)
Plugging in the values, we get:
s = (214 m/s)(8.2 s) + (1/2)(-9.8 m/s^2)(8.2 s)^2
Now, let's solve the equation step by step:
1. Multiply the initial velocity and time:
(214 m/s)(8.2 s) = 1750.8 m
2. Multiply the acceleration and the square of time:
(1/2)(-9.8 m/s^2)(8.2 s)^2 = -323.8296 m
3. Add the two results together to find the displacement:
1750.8 m + (-323.8296 m) = 1426.9704 m
Therefore, the displacement of the bullet after 8.2 seconds will be approximately 1426.9704 meters.