An enemy plane is flying horizontall at a distance of 2.0km with a speed of 340m/s.An army man with anti-craft gun on the ground sight the enemy with a muzzle speed at 60m/s .when the enemy plane is directly overhead.find
a)at what angle from the verticals should the gun be fired so as to hit the plane
b)at what minimum altitude should the enemy plane fly to aviod being hit(take g=10m/s^2)
The language is garbled. It sounds like the gun is to be fired when the plane is directly overhead. No joy there, since the bullet's speed is much slower than the plane's (?)
Is the gunner to fire so that he hits then plane when it is directly overhead?
Please proofread your post and make it read the way you got it.
An enemy plane is flying horizontally at an altitude of 2.0km with a speed of 340m/s.An
army man with anti-craft gun on the ground
sight the enemy with a muzzle speed at 60m/s
.when the enemy plane is directly
overheaded.find
a)at what angle from the verticals should the
gun be fired so as to hit the plane.
b)at what minimum altitude should the enemy
plane fly to avoid being hit(take g=10m/s^2)
To solve this problem, we need to consider the projectile motion of the bullet fired from the anti-aircraft gun. Let me explain how to approach each part of the question:
a) To calculate the angle from the vertical at which the gun should be fired, we can use the concept of relative velocity. The projectile motion of the bullet will be a superposition of its initial velocity and the velocity of the plane.
Let's break down the velocities:
- The horizontal velocity of the plane is given as 340 m/s.
- The muzzle velocity of the bullet fired from the anti-aircraft gun is given as 60 m/s.
Now, we can calculate the vertical component of the plane's velocity by using trigonometry. The angle from the vertical at which the gun should be fired is the same as the angle between the plane's velocity vector and the vertical.
To find this angle (θ), we can use the equation:
tan(θ) = vertical component of plane's velocity / horizontal component of plane's velocity
Vertical component of plane's velocity = plane's speed * sin(90°) = 340 m/s * sin(90°)
Remember, sin(90°) equals 1. So, the vertical component of the plane's velocity will simply be 340 m/s.
Similarly, the horizontal component of the plane's velocity is plane's speed * cos(90°) = 340 m/s * cos(90°)
Again, cos(90°) equals 0. So, the horizontal component of the plane's velocity will be 0 m/s.
Now we have the vertical and horizontal components of the plane's velocity, and the vertical component of the bullet's velocity (which is 60 m/s).
tan(θ) = 60 m/s / 340 m/s
Now, calculate θ by taking the inverse tangent of both sides:
θ = arctan(60 m/s / 340 m/s)
Use a calculator to find the inverse tangent (arctan) of 60 divided by 340. The result will be the angle from the vertical at which the gun should be fired.
b) To determine the minimum altitude at which the enemy plane should fly to avoid being hit, we need to analyze the time of flight of the bullet and the time taken by the plane to cross the vertical distance covered by the bullet.
First, calculate the time of flight of the bullet fired by the anti-aircraft gun using the formula:
time of flight = 2 * (vertical component of the plane's velocity) / acceleration due to gravity
Here, we need to consider the vertical component of the plane's velocity as the initial velocity, since we are calculating the time of flight. The acceleration due to gravity is given as 10 m/s^2.
Substitute the values:
time of flight = 2 * 340 m/s / 10 m/s^2
Simplify the equation and calculate the time of flight.
Now, calculate the time taken by the plane to cross the vertical distance covered by the bullet:
time taken by plane = vertical distance / vertical component of the plane's velocity
The vertical distance is the altitude at which the plane is flying.
Since we know the horizontal velocity of the plane is 340 m/s, we can determine how far the plane will travel during the time of flight of the bullet by multiplying the horizontal velocity by the time of flight.
Now, substitute the values into the equation:
time taken by plane = (horizontal velocity of the plane * time of flight) / vertical component of the plane's velocity
Calculate the time taken by the plane.
Finally, calculate the altitude at which the plane should fly to avoid being hit by taking the product of the time taken by the plane and the horizontal velocity of the plane.
By following these steps, you can find the angle from the vertical at which the gun should be fired to hit the plane and the minimum altitude at which the plane should fly to avoid being hit.