The pilot of an airplane traveling 160 km/h wants to drop supplies to flood victims isolated on a patch of land 160m below. The supplies should be dropped how many seconds before the plane is directly overhead?
isn't it
how long to fall 160 meters?
(1/2) g t^2 = 160 not
how long to fall 160 meters?
(1/2) g t^2 = 60
You're correct Lilly.
It's not a very good question anyway. It will fall in 5.7 seconds no matter how fast the thing is going. Who knows whether they get the supplies or not.
To find out how many seconds before the plane is directly overhead the supplies should be dropped, we'll need to calculate the time it takes for the supplies to fall from the plane to the ground.
First, let's convert the speed of the plane from km/h to m/s:
160 km/h = (160 * 1000) m/3600 s ≈ 44.44 m/s
Next, we need to determine the time it takes for the supplies to fall from the plane to the ground. We can use the equation of motion for free fall:
s = ut + (1/2)gt^2
Where:
s = distance (160 m)
u = initial velocity (0 m/s, since the supplies are dropped)
g = acceleration due to gravity (9.8 m/s^2)
t = time
Plugging in the values and solving for time:
160 = 0 * t + (1/2) * 9.8 * t^2
160 = 4.9t^2
t^2 = 160/4.9
t^2 ≈ 32.653
t ≈ √(32.653)
t ≈ 5.71 s
Therefore, the supplies should be dropped approximately 5.71 seconds before the plane is directly overhead the flood victims.
The horizontal speed of the supplies during the fall is the airplane speed (if you drop a bomb, then turn, because if you go straight it hits under you :)
so
how long to fall 160 meters?
(1/2) g t^2 = 60
t^2 = 120/g = 120/9.81
t = 3.5 seconds