an artlillery shell is fired with an initial velocity of 325 m/s at 55 degree above the horizontal.It explodes on a mountainside 42 sec after firing.What are the x and y coordinates of the shell where it explodes,relative to its firing point?
heres what I got
t=325(sin55)/9.8=33.2 sec.
the shell explodes 42-33.2 =8.8 sec
x=325(cos 55)42302 m
y max=v^2sin^2a/(9.8x2)=(0.99 x 325 x 325)/(2x 9.8)=5386.4
H=1/2 x 9.8 x (8.8)^2=379
therefore upon explosion on its way down the shell is 5386.4-379=5007 m
co-ordinates of the shell upon explosion y=5007 m
x=302 m
To find the x and y coordinates of the shell where it explodes, we can break down the problem into two components: the horizontal (x) and vertical (y) components.
First, let's calculate the time it takes for the shell to reach its maximum height. We can use the formula: t = V*sinθ / g, where V is the initial velocity (325 m/s), θ is the angle of projection (55 degrees), and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get:
t = 325 * sin(55) / 9.8 ≈ 33.2 s
Next, we subtract this time from the total time (42 s) to find the time it takes for the shell to explode after reaching its maximum height:
t_explosion = 42 s - 33.2 s ≈ 8.8 s
Now, let's calculate the x-coordinate of the shell where it explodes. We can use the formula: x = V*cosθ * t_explosion. Plugging in the values, we get:
x = 325 * cos(55) * 8.8 ≈ 302 m
So, the x-coordinate of the shell where it explodes is approximately 302 m.
Next, let's calculate the y-coordinate of the shell where it explodes. We'll first calculate the maximum height (y_max) reached by the shell using the formula: y_max = V^2 * sin^2(θ) / (2 * g). Plugging in the values, we get:
y_max = (325^2 * sin^2(55)) / (2 * 9.8) ≈ 5386.4 m
Then, we'll calculate the vertical distance (H) covered by the shell during the time it takes to explode (t_explosion) using the formula: H = (1/2) * g * t_explosion^2. Plugging in the values, we get:
H = (1/2) * 9.8 * 8.8^2 ≈ 379 m
Finally, we can calculate the y-coordinate of the shell where it explodes by subtracting the vertical distance covered by the shell on its way down (H) from the maximum height (y_max):
y_coordinate = y_max - H ≈ 5386.4 m - 379 m ≈ 5007 m
So, the y-coordinate of the shell where it explodes is approximately 5007 m.
Therefore, the coordinates of the shell where it explodes, relative to its firing point, are approximately (x = 302 m, y = 5007 m).