projectile motion question need help working through it
an airplane travelling 1001meters above the ocean at 125km/h is going to drop a box of supplies to shipwrecked victims below.
a) How many seconds before the plane is directly overhead should the box be dropped
b) what is the horizontal distance between the pane and the victims when the box is dropped?
LOL - answer b first.
The plane is going exactly as fast in the horizontal direction as the bomb. Therefore the plane is exactly over the bomb when it hits. When you drop a bomb, turn and bank after release.
Now for part a, how long does it take an object to fall 1001 meters?
distance = (1/2) g t^2
1001 = 4.9 t^2
solve for t
To solve this projectile motion problem, we can break it down into two components: vertical and horizontal.
a) Vertical Motion:
First, we need to determine the time it takes for an object to fall a given distance. In this case, the airplane is 1001 meters above the ocean, and we want to find how many seconds before the plane is directly overhead the box should be dropped.
We can use the equation for vertical motion: h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Rearranging the equation to solve for t, we get:
t = sqrt(2h/g)
Plugging in the values, we have:
t = sqrt(2 * 1001 m / 9.8 m/s^2)
t = sqrt(2002 m / 9.8 m/s^2)
t ≈ 14.23 seconds
Therefore, the box should be dropped approximately 14.23 seconds before the plane is directly overhead.
b) Horizontal Motion:
Next, we need to find the horizontal distance between the plane and the victims when the box is dropped.
We can use the formula for horizontal motion: d = vt, where d is the distance, v is the horizontal velocity, and t is the time.
To find the horizontal velocity, we need to convert the given speed from km/h to m/s:
v = 125 km/h * (1000 m/1 km) * (1 h/3600 s)
v ≈ 34.72 m/s
Plugging in the values, we have:
d = (34.72 m/s) * (14.23 s)
d ≈ 494.61 meters
Therefore, the horizontal distance between the plane and the victims when the box is dropped is approximately 494.61 meters.