A rescue plane has to drop supplies to a group of castaways who are stranded on a deserted island. The plane is flying as 150 m/s at a level altitude of 1200 m. How far ahead of the landing zone should the plane release the supplies?
I'm not even sure how to start this one. Could someone maybe tell me which step(s) I need to take?
Compute the time T required for the package to reach the ground, using
(1/2) gT^2 = H (altitude)
T = sqrt (2H/g)
Then use the horizontal equation of motion to get the distance d ahead of the target to release the sup-plies
d = V T = V sqrt (2H/g)
Thanks, I got it now. :)
To determine how far ahead of the landing zone the plane should release the supplies, you need to calculate the horizontal distance traveled by the plane during the time it takes for the supplies to reach the ground. Here are the steps you can follow to solve this problem:
1. Start by finding the time it takes for the supplies to fall to the ground. To do this, you can use the equation of motion for vertical motion:
h = (1/2) * g * t^2
Where:
- h is the initial vertical height (1200 m)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time it takes for the supplies to fall
Rearranging the equation to solve for time, t:
t = sqrt((2h) / g)
2. Substitute the given values into the equation to calculate the time:
t = sqrt((2 * 1200 m) / (9.8 m/s^2))
3. Calculate the time, t.
4. Now, you can calculate the horizontal distance traveled by the plane during this time. Since the plane is flying at a constant horizontal speed of 150 m/s:
Distance = Time * Horizontal speed
Distance = t * 150 m/s
5. Plug in the calculated value of time, t, into the equation to find the horizontal distance traveled by the plane.
By following these steps, you will be able to determine how far ahead of the landing zone the plane should release the supplies.