an enemy plane is flying horizontally at an altitude of 2.0Km,with a speed of 3.0m/s.an army man with a gun on the ground sights the enemy plane and fires a shell with a muzzle speed of 600m/s when d plane Is directly overhead.at what angle to the ground should the plane be fired so as to hit the plane??

To calculate the angle at which the army man should fire the gun to hit the enemy plane, we can follow these steps:

Step 1: Determine the time it takes for the shell to reach the altitude of the enemy plane.
Let's assume that the time taken is 't' seconds.

Step 2: Calculate the horizontal distance covered by the enemy plane during time 't'.
Given the horizontal speed of the enemy plane is 3.0 m/s, the horizontal distance covered is:
Distance = Speed × Time
Distance = 3.0 m/s × t

Step 3: Calculate the distance between the army man and the enemy plane when the shell reaches the same altitude.
Let's define this distance as 'd'.

Step 4: Calculate the time taken for the shell to reach distance 'd'.
The horizontal speed of the shell is constant, so the time taken is given by:
t = d / (600 m/s)

Step 5: Equate the time taken for the shell to reach altitude 2.0 km to the time taken for the shell to reach distance 'd'.
3.0 m/s × t = d / (600 m/s)

Step 6: Solve for 'd'.
We can substitute the value of 't' calculated in Step 5 into the equation, which gives us:
3.0 m/s × (d / (600 m/s)) = 2,000 m

Simplifying the equation:
d / 200 = 2,000 m
d = 200 × 2,000 m
d = 400,000 m

Step 7: Calculate the angle.
Using trigonometry, we can calculate the angle using the tangent of the angle:
tan(angle) = (2.0 km) / (400,000 m)

Simplifying the equation:
angle = arctan((2.0 km) / (400,000 m))

Calculating the value using a calculator, the angle is approximately 0.286 degrees.

Therefore, the army man should fire the gun at an angle of approximately 0.286 degrees to the ground in order to hit the enemy plane.

To determine at what angle the plane should be fired to hit it, we need to consider the horizontal and vertical components of the motion.

Let's break down the problem:

1. Initial Conditions:
- The enemy plane is flying horizontally at an altitude of 2.0 km, which is equivalent to 2000 meters.
- The plane's speed is 3.0 m/s.

2. Determine the time it takes for the shell to reach the height of the plane:
- We know that the muzzle speed of the shell is 600 m/s.
- The time taken to reach a certain height can be calculated using the equation of motion: h = ut + (1/2)gt^2, where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time.
- In this case, the initial velocity, u, is 0 m/s because the shell is fired vertically upward.
- The height, h, is given as 2000 meters.
- The acceleration due to gravity, g, is approximately 9.8 m/s^2.
- Rearranging the equation, we get t^2 = (2h / g), so t = √(2h / g).

3. Calculate the time it takes for the shell to reach the plane horizontally:
- The horizontal distance traveled by the plane during the shell's ascent time is given by the equation: d = v*t, where d is the distance, v is the velocity, and t is the time.
- In this case, the velocity, v, is 3.0 m/s, and the time, t, is the value we obtained in step 2.

4. Determine the angle to the ground:
- The angle to the ground can be calculated using the trigonometric relation: tan(theta) = (height / distance).
- In this case, the height is 2000 meters (given) and the distance is the value we calculated in step 3.

Now, let's plug in the values and find the answer:

1. Calculate the time it takes for the shell to reach the height of the plane:
- t = √(2h / g)
- t = √(2 * 2000 / 9.8)
- t ≈ 20.2 seconds (rounded to 2 decimal places)

2. Calculate the time it takes for the shell to reach the plane horizontally:
- d = v * t
- d = 3.0 * 20.2
- d ≈ 60.6 meters (rounded to 1 decimal place)

3. Determine the angle to the ground:
- tan(theta) = (height / distance)
- tan(theta) = (2000 / 60.6)
- theta ≈ tan^(-1)(33.00)
- theta ≈ 67.7 degrees (rounded to 1 decimal place)

Therefore, the army man should fire the gun at an angle of approximately 67.7 degrees to hit the enemy plane.