You are a general in the Napoleonic war. The battle has taken you to a trench 7m deep. You have a mortar that will fire an explosive at a speed of 200 m/s at an angle of 80. You have a low flying reconnaissance airplane scouting out the enemy troops at a height of 500 m. Your pilot does not want to fly in the path of your bomb. What distance from your camp would your pilot be well advised to avoid?

Question

You are a general in the Napoleonic war. The battle has taken you to a trench 7m deep. You have a mortar that will fire an explosive at a speed of 200 m/s at an angle of 80. You have a low flying reconnaissance airplane scouting out the enemy troops at a height of 500 m. Your pilot does not want to fly in the path of your bomb. What distance from your camp would your pilot be well advised to avoid?

Answer 1

Range = Vo^2*sin(2A)/g

200^2*sin(160)/9.8 = 1396 m.

Answer 2

To determine the distance that the pilot should avoid to stay clear of the bomb's path, we need to calculate the range of the mortar. The range is the horizontal distance covered by the projectile. In this case, the range can be calculated using the initial speed of the explosive and the launch angle.

To begin, we need to break down the initial speed into its horizontal and vertical components. The horizontal component (Vx) represents the speed in the x-direction (parallel to the ground), while the vertical component (Vy) represents the speed in the y-direction (perpendicular to the ground).

Using trigonometry, we can calculate the components as follows:

Vx = initial speed * cos(angle)
Vy = initial speed * sin(angle)

In this case:
Angle (θ) = 80 degrees
Initial speed (Vi) = 200 m/s

Vx = 200 m/s * cos(80 degrees)
Vy = 200 m/s * sin(80 degrees)

Next, we can calculate the time it takes for the explosive to reach the ground. Since the explosive and the airplane are both released at the same time, the time is the same for both of them.

To calculate the time of flight (t), we can use the vertical component of velocity (Vy):

t = Vertical distance / Vy

In this case:
Vertical distance (h) = 500 m
Vy = 200 m/s * sin(80 degrees)

t = 500 m / (200 m/s * sin(80 degrees))

Finally, we can calculate the range (R) using the horizontal component of velocity (Vx) and the time of flight (t):

R = Vx * t

In this case:
Vx = 200 m/s * cos(80 degrees)
t = 500 m / (200 m/s * sin(80 degrees))

R = (200 m/s * cos(80 degrees)) * (500 m / (200 m/s * sin(80 degrees)))

Calculating these values, we can find the range of the mortar. This will give us the distance from the camp that the pilot should avoid to stay clear of the bomb's path.