a rifle is fried from the top of a building 220 meters high with an initial velocity of 425 m/s at an angle of 12.0 degrees above the horizontal.
a. how long will it take for the bullet to reach the ground?
b. how far from the base of the building will the bullet strike the ground?
c. what will be the velocity of the bullet just as it reaches te ground?
a. you do v^2 = vi^2 = 2aD
then u do V= vi + at to get time as 20.3
b. D= Vox*T (415.7)(20.3) = 8440m
c.430m/s at 14.8* downward
To solve these problems, we can break down the initial velocity into horizontal and vertical components. The horizontal component will remain constant throughout the motion, while the vertical component will be affected by gravity.
a. To find the time it takes for the bullet to reach the ground, we need to calculate the time it takes for the vertical component of the velocity to become zero. We can use the following equation for vertical motion:
vf = vi + at
Here, vf is the final vertical velocity, vi is the initial vertical velocity, a is the acceleration due to gravity (-9.8 m/s^2), and t is the time. Since the bullet starts from rest when it reaches the ground, the final vertical velocity will be zero. The initial vertical velocity can be found using the given information about the initial velocity and the angle.
vi = v * sin(theta)
Substituting the values, we get:
0 = vi + at
0 = (v * sin(theta)) - (9.8 * t)
Solving for t, we get:
t = (v * sin(theta)) / 9.8
Now, substitute the given values to find the time it takes for the bullet to reach the ground.
b. To find the horizontal distance from the base of the building where the bullet strikes the ground, we can use the equation for horizontal motion:
d = vi * t + (0.5 * a * t^2)
Here, d is the horizontal distance, vi is the initial horizontal velocity, t is the time, and a is the acceleration (which is zero in horizontal motion).
The initial horizontal velocity can be found using the given information about the initial velocity and the angle:
vi = v * cos(theta)
Substitute the values into the equation, and you will get the horizontal distance.
c. The final velocity of the bullet just as it reaches the ground can be found by using the equation:
vf = sqrt((vi^2) + (2 * a * d))
Here, vf is the final velocity, vi is the initial velocity, a is the acceleration (which is -9.8 m/s^2), and d is the vertical displacement (which is the height of the building, 220 meters).
Substitute the given values into the equation, and you will get the final velocity as the bullet reaches the ground.
Remember to use the appropriate units and to pay attention to the sign conventions when solving these equations.