A airplane has a speed of 290 km/h and is driving at an angle of 30 degrees below the horizontal when the pilot releasese a radar decoy. The horizontal distance between the release point and where the decoy hits the ground is 700m. a) How long is the decoy in the air? b) How high was the release point?
My teacher gave us the answer since we ran out of time. He said a) is 10 seconds and b) is 879m. Can you explain how I can get these answers? We have to know how to solve this type of proble for a quiz soon.
Figure the horizontal and vertical components of the airplane speed. The vertical speed is the initial vertical speed of the decoy. That speed is down, or negative.
The horizontal speed is the initial horizontal speed of the decoy.
Horizontaldistance=speedhorizontal*time
solve for time.
Now, having that time,
distancetoground=Speedvertical*time -1/2 g time^2
solve this for the vertical distance to the ground.
To solve this problem, we will first break down the given information and use the principles of projectile motion to find the answers.
a) How long is the decoy in the air?
1. Determine the horizontal and vertical components of the airplane's speed:
The given speed of the airplane is 290 km/h. We need to find the horizontal and vertical components of this speed.
The horizontal component can be found using the angle at which the airplane is flying. The angle is given as 30 degrees below the horizontal.
Horizontal component = Speed * Cosine(angle)
Horizontal component = 290 km/h * cos(30 degrees)
2. Calculate the time of flight for the decoy:
The horizontal distance between the release point and the point where the decoy hits the ground is given as 700m.
We can use this information along with the horizontal component of the airplane's speed to calculate the time of flight.
Horizontal distance = Horizontal component * Time
700m = Horizontal component * Time
Solve for time:
Time = 700m / Horizontal component
b) How high was the release point?
1. Calculate the vertical component of the airplane's speed:
The given speed of the airplane is 290 km/h. We need to find the vertical component of this speed.
The vertical component can be found using the angle at which the airplane is flying.
Vertical component = Speed * Sine(angle)
Vertical component = 290 km/h * sin(30 degrees)
2. Calculate the vertical distance from the release point to the ground using the calculated time of flight:
We can use the formula for vertical projectile motion to find the vertical distance.
Vertical distance = Vertical component * Time - 1/2 * g * Time^2
Where g is the acceleration due to gravity, approximately 9.8 m/s^2.
Solve for the vertical distance.
By following these steps, we can calculate both the time of flight and the height of the release point. Plugging in the values into the equations will give you the final answers, which are given by your teacher as 10 seconds for the time of flight and 879m for the height of the release point.