Final answer:
The time taken for the food package to reach the ground is 10 seconds, and the horizontal distance traveled is 2000 meters.
Step-by-step explanation:
To find the values of t (time) and d (horizontal distance) when a food package is dropped from an airplane, we can use the equations of motion. Since the package is dropped vertically, the vertical component of its velocity is the same as the final vertical velocity, which is given by v = gt.
Given that the height is 500m and the acceleration due to gravity is 10ms^2, we can calculate the time it takes for the package to reach the ground using the formula h = 0.5gt^2. Plugging in the values, we get:
500 = 0.5 * 10 * t^2
Simplifying the equation further, we get t^2 = 100, which gives us t = 10s.
Now, to find the horizontal distance traveled by the package, we can use the equation d = vt, where v is the horizontal component of the velocity. Since the airplane is flying at a constant speed of 200ms, the horizontal component of the velocity is also 200ms. Plugging in the values, we get:
d = 200 * 10 = 2000m.