A bullet is fired from a rifle that is held 2.0 m above the ground in a horizontal position. The initial speed of the bullet is 1250 m/s.
(a) Find the time it takes for the bullet to strike the ground.
1 s
(b) Find the horizontal distance traveled by the bullet.
2 m
To find the time it takes for the bullet to strike the ground, we can use the equation of motion for vertical motion:
h = ut + (1/2)gt^2
where:
h = initial height = 2.0 m (from the ground)
u = initial vertical velocity = 0 m/s (since the bullet is fired horizontally)
g = acceleration due to gravity = 9.8 m/s^2 (assuming the motion takes place near the surface of the Earth)
t = time
Plugging in the values, the equation becomes:
2.0 = 0 * t + (1/2) * 9.8 * t^2
Simplifying, we get:
2.0 = 4.9 * t^2
Dividing both sides of the equation by 4.9, we get:
t^2 = 2.0 / 4.9
t^2 ≈ 0.408
Taking the square root of both sides, we get:
t ≈ √0.408
t ≈ 0.64 s
Therefore, it takes approximately 0.64 seconds for the bullet to strike the ground.
To find the horizontal distance traveled by the bullet, we can use the equation of motion for horizontal motion:
s = ut
where:
s = horizontal distance traveled
u = initial horizontal velocity = 1250 m/s (given)
t = time
Plugging in the values, the equation becomes:
s = 1250 * 0.64
s ≈ 800 m
Therefore, the horizontal distance traveled by the bullet is approximately 800 meters.