Welcome to the article An artillery shell is fired with an initial velocity of 328 m s at an angle above the horizontal It explodes on a mountainside 42. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
(a) The x coordinate of the shell where it explodes is approximately 13,897.6 m.
(b) The y coordinate of the shell where it explodes is approximately -6,994.9 m.
(c) The x component of its velocity just before it hits the mountainside is approximately 139.9 m/s.
(d) The y component of its velocity just before it hits the mountainside is approximately -328 m/s.
To determine the x coordinate where the shell explodes, we can use the equation:
x = v0x * t
where v0x is the initial x component of the velocity and t is the time of flight. Since the shell is fired above the horizontal, the initial y component of the velocity is zero, and the x component remains constant throughout its trajectory. The initial velocity can be broken down into its x and y components using trigonometry:
v0x = v0 * cos(theta)
v0y = v0 * sin(theta)
where v0 is the initial velocity and theta is the launch angle. However, since the launch angle is not given in the question, we cannot directly calculate v0x. Hence, we assume that the launch angle is 45 degrees, which yields v0x = v0y = 328 m/s.
Using the given time of flight (t = 42.1 s), we can now calculate the x coordinate:
x = (328 m/s) * (42.1 s) = 13,797.6 m
To determine the y coordinate where the shell explodes, we can use the equation:
y = v0y * t + (1/2) * g * t^2
where g is the acceleration due to gravity. Since the shell explodes on the mountainside, we assume it hits the same height as the firing point, resulting in a change in elevation of zero. Therefore, the y coordinate of the shell where it explodes is the same as the y coordinate at the firing point, which is zero.
The x component of the velocity just before it hits the mountainside remains constant and equal to the initial x component, i.e., approximately 139.9 m/s. The y component of the velocity just before it hits the mountainside can be found using the equation:
[tex]v = v0y + g * t[/tex]
where v is the y component of the velocity. Substituting the values:
[tex]v = (328 m/s) - (9.8 m/s^2) * (42.1 s) = -326.2 m/s[/tex]
Therefore, the y component of the velocity just before it hits the mountainside is approximately -326.2 m/s.
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