9. H SSM From the top of a tall building, a gun is fi red. The bullet leaves
the gun at a speed of 340 m/s, parallel to the ground. As the drawing shows,
the bullet puts a hole in a window of another building and hits the wall that
faces the window. Using the data in the drawing, determine the distances D
and H, which locate the point where the gun was fi red. Assume that the bullet
does not slow down as it passes through the window.
I don't see a drawing but perhaps the smart tutors on this site can use the description to figure it out.
If the bullet flew for time t seconds,
the vertical speed is -9.8t
the horizontal speed is 340
the vertical drop is -4.9t^2
the horizontal distance is 340t
and why do you always type "fi red" instead of "fired"?
To determine the distances D and H, we need to use the kinematic equations to analyze the motion of the bullet.
Let's break down the problem step by step:
Step 1: Identify the given information
From the problem statement, we are given:
- Initial velocity of the bullet (v₀) = 340 m/s
- The bullet hits the wall which is at a distance D from the window
- The height of the window from the ground is H
Step 2: Determine the time of flight
Since the bullet moves parallel to the ground, we can treat its motion as projectile motion in the horizontal direction. In projectile motion, the time of flight (t) is the same for both horizontal and vertical components.
To find the time of flight, we'll use the horizontal component of motion. The horizontal distance D is equal to the horizontal velocity (v₀) multiplied by the time of flight (t):
D = v₀ * t
Rearranging this equation, we find the time of flight:
t = D / v₀
Step 3: Find the vertical distance covered by the bullet
Since the bullet is fired horizontally, there is no initial vertical velocity. Therefore, the vertical motion of the bullet is solely due to gravity.
We can use the equation of motion for vertical motion:
H = 0.5 * g * t²
where g is the acceleration due to gravity (approximately 9.81 m/s²).
Substituting the value of t from Step 2 into this equation, we can solve for H.
Step 4: Solve for D and H
Now, we can substitute the given values into the equations:
t = D / v₀
H = 0.5 * g * t²
Using these equations, we can calculate the values of D and H.