A bullet is fired horizontally with a velocity of 250 m/s from the top of a building 100m high. Find the Horizontal and vertical velocities of the bullet when it reaches the ground, the resultant velocity, the horizontal displacement, the net displacement, the direction of the net displacement.
find how long it takes the bullet to fall 100m:
4.9 t^2 = 100
Knowing that value of t, the bullet travels 250t meters horizontally, and its downward speed is 9.8t m/s.
Now you can draw a diagram and figure the other values.
To find the horizontal and vertical velocities of the bullet when it reaches the ground, the resultant velocity, the horizontal displacement, the net displacement, and the direction of the net displacement, we can apply the laws of kinematics and analyze the projectile motion.
Let's start by finding the time it takes for the bullet to reach the ground. Since the bullet is fired horizontally, its initial vertical velocity is 0 m/s. We can use the equation:
h = ut + (1/2)gt²
where:
h = vertical displacement (100 m)
u = initial vertical velocity (0 m/s)
g = acceleration due to gravity (-9.8 m/s²)
t = time
Rearranging the equation, we can solve for t:
100 = 0*t + (1/2)*(-9.8)*t²
100 = -4.9t²
t² = 100/-4.9
t² ≈ 20.41
t ≈ √20.41
t ≈ 4.52 s
So, it takes approximately 4.52 seconds for the bullet to reach the ground.
Now, let's find the horizontal velocity of the bullet. Since it's fired horizontally, the horizontal velocity remains constant throughout the motion. Therefore, the horizontal velocity is 250 m/s.
To calculate the vertical velocity when the bullet reaches the ground, we use the equation:
v = u + gt
where:
v = final vertical velocity
u = initial vertical velocity (0 m/s)
g = acceleration due to gravity (-9.8 m/s²)
t = time (4.52 s)
v = 0 + (-9.8)*4.52
v ≈ -44.296 m/s
The negative sign indicates that the bullet is moving downward with a velocity of approximately 44.296 m/s when it reaches the ground.
To find the resultant velocity, we can use the Pythagorean theorem:
resultant velocity = √((horizontal velocity)² + (vertical velocity)²)
resultant velocity = √((250)² + (-44.296)²)
resultant velocity ≈ 253.9 m/s
The horizontal displacement of the bullet can be calculated by using:
horizontal displacement = (horizontal velocity) * (time)
horizontal displacement ≈ (250 m/s) * (4.52 s)
horizontal displacement ≈ 1130 m
The net displacement can be determined by combining the horizontal and vertical displacements. Since the bullet is fired horizontally, the vertical displacement is zero.
Therefore, the net displacement is equal to the horizontal displacement, which is approximately 1130 m.
Lastly, the direction of the net displacement is horizontally, along the direction of the bullet's initial velocity.