A bullet is fired straight up from a gun with a
muzzle velocity of 235 m/s.
Neglecting air resistance, what will be its
displacement after 5.7 s? The acceleration of
gravity is 9.8 m/s
2
.
Answer in units of m
d=vi*t-4.9t^2
To find the displacement of the bullet after 5.7 s, we can use the kinematic equation:
displacement = initial velocity * time + (1/2) * acceleration * time^2
First, let's calculate the initial velocity (u) of the bullet, which is given as 235 m/s.
Next, we need to determine the acceleration (a) of the bullet, which is equal to the acceleration due to gravity, 9.8 m/s^2, and is acting in the opposite direction to the motion of the bullet.
Finally, we substitute these values into the formula:
displacement = (235 m/s) * (5.7 s) + (1/2) * (-9.8 m/s^2) * (5.7 s)^2
Calculating this expression will give us the displacement of the bullet after 5.7 s.
To find the displacement of the bullet after 5.7 seconds, we need to calculate its initial velocity and the time it takes to reach its highest point. Then, we can use the kinematic equation to find the displacement.
First, let's find the time it takes for the bullet to reach its highest point. In this case, the bullet is fired straight up, so it will reach its highest point when its vertical velocity becomes zero. We can use the following equation to calculate the time (t) it takes to reach the highest point:
v = u + at
Where:
v = final velocity (0 m/s since it reaches its highest point)
u = initial velocity (given as 235 m/s)
a = acceleration (in this case, the acceleration due to gravity, -9.8 m/s^2 since it acts in the opposite direction)
t = time
Rearranging the equation, we have:
t = (v - u) / a
t = (0 - 235) / -9.8
t = 24.49 s
Next, let's find the displacement of the bullet during this time. As the bullet reaches its highest point, it will start to fall down. The displacement during this time can be calculated using the following equation:
s = ut + 0.5at^2
Where:
s = displacement
u = initial velocity (given as 235 m/s)
t = time (24.49 s)
a = acceleration (in this case, the acceleration due to gravity, -9.8 m/s^2)
Substituting the values into the equation:
s = (235 * 24.49) + 0.5 * (-9.8) * (24.49)^2
s = 5739.15 m
Thus, the displacement of the bullet after 5.7 seconds is 5739.15 m.