An anti-aircraft gun fires at an elevation of 60 degree at an enemy aircraft at 10000m above the ground. At what speed must the cannon be shot to hit the plane at that height? (g=9.8)
1/2 m (v sin(60º)^2 = m g 10 km
v = √(g * 20 km) / sin(60º)
this is the minimum velocity for the projectile to reach the height of the plane ... faster would be better
Good
An anti air craft gun fires at an elevation of 60 degree at an enemy air craft at 1000m above the plane at the height (g=9.8ms2
an anti aircraft fires at an elevation of 60degrees at an enemy aircraft at 10000m above d ground. at what speed must the cannon be shot to hit the plane at that height. take g as 9.8m/s
To solve this problem, we can use the principles of projectile motion. The following steps will guide you on how to get the speed at which the cannon must be shot to hit the aircraft at the given height:
Step 1: Understand the problem:
In this scenario, the anti-aircraft gun is firing at an elevation of 60 degrees. We are required to find the speed at which the cannon must be shot to hit the plane at a given height of 10,000m above the ground. The value of acceleration due to gravity, g, is given as 9.8 m/s^2.
Step 2: Break down the problem:
Given that we want to find the initial speed (or velocity) of the projectile fired from the cannon, we need to utilize the equations of projectile motion.
Step 3: Analyze the initial vertical motion:
Since the cannon is fired at an elevation of 60 degrees, we can decompose the initial velocity into its vertical and horizontal components.
The initial vertical velocity, V_y, can be determined using trigonometric functions. In this case:
V_y = V * sin(θ), where V is the initial velocity and θ is the elevation angle (60 degrees).
Step 4: Determine the time of flight:
In projectile motion, the time taken by the object to reach the maximum height is equal to the time taken to return to the same vertical position. This is called the time of flight, denoted as t_total.
t_total = 2 * (V_y) / g
Step 5: Calculate the vertical displacement:
The vertical displacement, Δy, is the height at which we want to hit the aircraft. In this case, Δy = 10,000m.
Step 6: Find the initial horizontal velocity:
The horizontal velocity, V_x, remains constant throughout the projectile's motion. So we can calculate it using the horizontal distance and time of flight:
V_x = Δx / t_total
Step 7: Calculate the initial speed:
The initial speed can be found by combining the horizontal and vertical components of the velocity:
V = sqrt(V_x^2 + V_y^2)
Step 8: Plug in the values and solve the equation:
Now, you can substitute the values into the equations obtained in the previous steps and calculate the initial speed.
V = sqrt((Δx / t_total)^2 + (V * sin(θ))^2)
Simplify and solve this equation for V (initial speed) using algebraic manipulations.
By following these steps, you can determine the speed at which the cannon must be shot to hit the plane at the given height of 10,000m above the ground.