an anti aircraft gun fires at an elevation of 60 degree at an enemy air at 10.000 m above the ground. AE what speed must cannombe shot to hit the plane at the height (g=10m50)
To determine the speed at which the cannon must be shot to hit the plane at a certain height, we can use the principles of projectile motion.
Let's break down the problem:
1. We are given the angle of elevation of the anti-aircraft gun, which is 60 degrees.
2. The plane is flying at a height of 10,000 meters above the ground.
3. The gravitational acceleration (g) is given as 10 m/s^2.
To solve for the speed at which the cannon must be shot, we need to consider two components: horizontal and vertical.
1. Horizontal Component:
The horizontal component of the projectile's velocity remains constant throughout its motion. This means that the horizontal speed remains the same from the point of firing until the point of hitting the plane.
Therefore, the horizontal component of the projectile's initial velocity is given by:
Velocity (horizontal) = Velocity (initial) * cos(angle of elevation)
2. Vertical Component:
The vertical component of the velocity changes due to the acceleration caused by gravity. At the highest point of the projectile's trajectory, the vertical component of the velocity becomes zero.
We can calculate the time it takes for the projectile to reach its maximum height using the equation:
time taken to reach max height = v (vertical) / g
The initial vertical velocity can be calculated as:
v (vertical) = Velocity (initial) * sin(angle of elevation)
Substitute the value of v (vertical) into the time equation to solve for the time taken to reach maximum height.
Since the time taken to reach maximum height is half of the total time of flight, we can double the time to find the total time of flight:
total time of flight = 2 * time taken to reach max height
With the total time of flight, we can use it to calculate the vertical displacement of the projectile using the equation:
vertical displacement = v (vertical) * total time of flight - (0.5) * g * (total time of flight)^2
Now we have the vertical displacement, and we know that it should be equal to 10,000 meters (the height of the plane).
Setting the vertical displacement equal to 10,000 meters and solving for Velocity (initial), we can find the speed at which the cannon must be shot to hit the plane at the given height.