An artillery shell is fired with a minimal velocity of 400 m/s at 54 deg above the horizontal. To clear an avalanche, it explodes on a mountain side 40 s after firing.
What is the X-coordinate relative to it's firing point? What is the Y-coordinate?
What do you mean by minimal velocity?
Is 400 m/s the initial velocity or not?
If it is, 400 cos54 = 235.1 m/s is the horizontal V component, which remains constant. The X coordinate of the impact point is therefore 235.1x40 = 9405 m.
For the Y coordinate, solve
Y = 400 sin54 *t - (g/2) t^2
with t = 40 s.
To find the X-coordinate and Y-coordinate relative to the firing point, we'll need to break down the projectile motion into its horizontal and vertical components.
First, let's find the horizontal component. The initial velocity of the artillery shell is given as 400 m/s. Since it's fired at an angle of 54 degrees above the horizontal, we can find the horizontal component by multiplying the initial velocity by the cosine of the launch angle:
Horizontal component = 400 m/s * cos(54°)
Next, let's find the vertical component. The initial velocity is given as 400 m/s, and the launch angle is 54 degrees. We can find the vertical component by multiplying the initial velocity by the sine of the launch angle:
Vertical component = 400 m/s * sin(54°)
Now, let's find the time it takes for the artillery shell to reach the mountain side. The time is given as 40 seconds after firing. Since the motion is symmetric, we can assume that it takes the same amount of time to reach the highest point and then fall back down. Therefore, the time to reach the mountain side is half of the given time:
Time = 40 s / 2
Now, we can use the horizontal component of velocity and time to find the X-coordinate relative to the firing point:
X-coordinate = Horizontal component * Time
Similarly, we can use the vertical component of velocity and time to find the Y-coordinate relative to the firing point:
Y-coordinate = Vertical component * Time - (1/2) * acceleration due to gravity * Time^2
The acceleration due to gravity can be taken as -9.8 m/s^2 since it acts downward.
Now we can substitute the values into the equations and calculate the results.