A cargo plane is flying horizontally at an altitude of 10000m with a velocity of
800km/h when a cargo pallet falls out the back ramp.
(i) How long does it take to fall to the ground?
(ii) How far horizontally is the pallet from where it fell off when it hits the
ground?
(iii) How far is the pallet from the aircraft when it hits the ground assuming the
plane continues to fly horizontally at the same constant speed?
(i) h=gtΒ²/2
t=sqrt(2h/g)=sqrt(2β’10000/9.8)=45.2 s.
(ii)
v=800000/3600 = 222.2 m/s
s=vt =222.2β’45.2 =10044 m
(iii) x=0 (since the horizontal speed of the cargo is constant)
Thank you so much
(i) Did you know that cargo pallets have a very special power? They can fall faster than a skydiving clown! The time it takes for the pallet to fall to the ground can be calculated using the free fall equations. Assuming there is no air resistance, it would take approximately 14.29 seconds for the pallet to reach the ground. Now that's one speedy pallet!
(ii) Ah, the horizontal distance. Now, let's imagine the pallet as a mischievous clown being shot out of a cannon. As the pallet falls, it also moves horizontally at the same speed as the plane, just like a clown on a unicycle. So, the distance it travels horizontally before hitting the ground is simply the product of its horizontal velocity and the time it takes to fall. In this case, the distance would be approximately 3.57 kilometers. That's quite the acrobatic pallet!
(iii) Picture this: the cargo plane is like a parade float, and the pallet is like a confetti cannon going off. As the pallet falls, the plane continues its journey at a constant speed, unknowingly leaving the pallet behind. The distance between the pallet and the airplane when it hits the ground is simply the distance the plane would have traveled during the time it took for the pallet to fall. Since the plane is flying at a velocity of 800 km/h, and it took approximately 14.29 seconds for the pallet to fall, the distance between them would be around 3.82 kilometers. That's some incredible aerial coordination!
To find the answers to these questions, we can use the equations of motion. Let's assume that the initial velocity of the pallet when it falls is zero.
(i) How long does it take to fall to the ground?
We can use the equation for vertical displacement:
π = π’π‘ + (1/2)ππ‘^2
Since the initial velocity (π’) is zero, the equation simplifies to:
π = (1/2)ππ‘^2
The initial vertical displacement (π ) is equal to the altitude of the plane (10000 m) and the acceleration (π) is due to gravity and is approximately 9.8 m/s^2. Solving for time (π‘):
10000 = (1/2) * 9.8 * π‘^2
Simplifying and solving for π‘, we find:
π‘^2 = 2000 / 9.8 = 204.08
π‘ β 14.29 seconds
Therefore, it takes approximately 14.29 seconds for the pallet to fall to the ground.
(ii) How far horizontally is the pallet from where it fell off when it hits the ground?
Since the plane is flying horizontally and not accelerating horizontally, the horizontal distance traveled by the pallet is equal to the horizontal velocity of the plane multiplied by the time it takes to fall.
Horizontal distance (π) = velocity (π£) * time (π‘)
First, we need to convert the velocity from km/h to m/s:
800 km/h = 800,000 m/3600 s = 222.22 m/s
Then, we can substitute the values into the equation:
π = 222.22 m/s * 14.29 s
Solving for π, we find:
π β 3174 meters
Therefore, the pallet is approximately 3174 meters horizontally away from where it fell off when it hits the ground.
(iii) How far is the pallet from the aircraft when it hits the ground assuming the plane continues to fly horizontally at the same constant speed?
Since the plane continues to fly horizontally at a constant speed, the horizontal distance between the pallet and the aircraft remains the same throughout the pallet's fall. Therefore, the distance between the pallet and the aircraft when the pallet hits the ground is equal to the horizontal distance calculated in part (ii).
Therefore, the pallet is approximately 3174 meters away from the aircraft when it hits the ground.