1. A rescue plane flying horizontally at an altitude of 500 m and velocity of 300 m\s east drops a food supply packet to plane crash survivors on the ground. The packet falls freely to the ground without a parachute. Assume that the weather is perfect.
a. Calculate the time it takes for the supply packet to hit the ground
b. Calculate horizontal distance
First note that the plane and the packet have the same horizontal velocity throughout this problem. Therefore the bomb lands exactly under the plane. If the package were a bomb, it would be wise to turn after yelling "bombs away".
anyway:
The falling problem:
falls 500 meters with zero initial vertical velocity component.
500 = (1/2) g t^2
1000 = 9.81 t^2
t = 10.1 seconds to fall 500 meters
Then the package flew for 10.2 seconds at a horizontal speed of 300 east so
d = u t = 300*10.1 = 3029 meters east
To calculate the time it takes for the supply packet to hit the ground, we can use the formula for the time of flight of an object in free fall:
t = √(2h/g)
where:
t is the time of flight,
h is the altitude or height from which the packet is dropped,
g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).
In this case, the altitude or height (h) is given as 500 m. So, we can substitute the values into the formula to find the time:
t = √(2 * 500 m / 9.8 m/s^2)
t = √(102.04 s^2)
t ≈ 10.1 s
Therefore, the time it takes for the supply packet to hit the ground is approximately 10.1 seconds.
To calculate the horizontal distance traveled by the supply packet, we can use the formula for horizontal distance (d) traveled by an object in free fall:
d = v * t
where:
d is the horizontal distance,
v is the horizontal velocity (300 m/s east).
t is the time of flight (10.1 seconds in this case).
Substituting the given values into the formula, we get:
d = 300 m/s * 10.1 s
d ≈ 3030 m
Therefore, the horizontal distance traveled by the supply packet is approximately 3030 meters.