A rifle bullet is fired vertically with initial speed 490 m/s. how long does it take the bullet to reach its greatest height?
At time t when
Vo - gt = 0
Vo = 490 m/s
g = 9.8 m/s^2
Solve for t.
50
To find the time it takes for the bullet to reach its greatest height, we need to consider the projectile motion of the bullet.
When a bullet is fired vertically, the only force acting on it is gravity. As a result, the bullet will accelerate downwards at a constant rate due to gravity (9.8 m/s^2).
Let's break down the motion of the bullet:
1. Initially, the bullet is fired vertically upwards with a velocity of 490 m/s.
2. As the bullet moves upward, it slows down due to the influence of gravity until it reaches its highest point (i.e., when its velocity becomes zero).
3. Finally, the bullet falls back to the ground, accelerating downwards due to gravity.
Now, in order to find the time it takes for the bullet to reach its greatest height, we can use the following equation of motion:
v = u + at
where:
v = final velocity (0 m/s, since the bullet reaches its highest point)
u = initial velocity (490 m/s)
a = acceleration (-9.8 m/s^2, as gravity is acting downwards)
t = time (the unknown we want to find)
Using the equation and rearranging it to solve for time (t), we get:
t = (v - u) / a
Substituting the values:
t = (0 - 490) / (-9.8)
t = 50 seconds
Therefore, it takes 50 seconds for the bullet to reach its greatest height.