An airplane is flying level at 80 m above the ground with a speed of 350 km/h max wishes to drop food and medical supplies to hit a target on the ground I want horizontal distance from the target should max release the supplies The answer is 393
.12 km.
To calculate the horizontal distance from the target that the supplies should be dropped, we can use the formula for projectile motion:
\(s = ut + 0.5at^2\),
where:
- s is the distance traveled horizontally,
- u is the initial horizontal velocity of the supplies (which is the same as the horizontal component of the airplane's velocity),
- a is the horizontal acceleration of the supplies (which is 0 since there is no horizontal force acting on the supplies once they are dropped),
- t is the time it takes for the supplies to hit the ground.
We can calculate the time it takes for the supplies to hit the ground using the formula:
\(s = ut + 0.5gt^2\),
where:
- s is the vertical distance the supplies are dropped (80 m in this case),
- u is the initial vertical velocity of the supplies (which is 0 since they are dropped),
- g is the acceleration due to gravity (9.81 m/s^2),
- t is the time it takes for the supplies to hit the ground.
Substitute the values into the equation:
\(80 = 0.5 * 9.81 * t^2\),
\(t = \sqrt{\frac{160}{9.81}} = 4.02\) (approximately).
Now, we can calculate the horizontal distance:
\(s = 350 \frac{km}{h} * \frac{1000m}{1km} * \frac{1h}{3600s} * 4.02 = 393.12m = 0.39312km\).
Therefore, the horizontal distance from the target that the supplies should be dropped is 0.39312 km or approximately 393 meters.