A car sits in the parking lot. Above is a cargo plane, flying horizontally at 61 m/s. At the exact moment the plane is 182 m directly above the car, a crate accidentally falls from its cargo doors. Relative to the car, where will the crate land? Enter m as unit and use g = 10. m/s2.

Question

A car sits in the parking lot. Above is a cargo plane, flying horizontally at 61 m/s. At the exact moment the plane is 182 m directly above the car, a crate accidentally falls from its cargo doors. Relative to the car, where will the crate land? Enter m as unit and use g = 10. m/s2.

Answer 1

how long does it take to hit the ground?

182=1/2 g t^2 solve for time t.

then, how far does it go horizontally.
d=61*t

Answer 2

To determine where the crate will land relative to the car when it falls from the cargo plane, we need to consider the horizontal and vertical components separately.

Horizontal Component:
Since the cargo plane is flying horizontally, the horizontal motion of the crate will not be affected by the plane's velocity. Therefore, the crate will land directly below the position where it was dropped.

Vertical Component:
To analyze the vertical motion of the crate, we can use the kinematic equation for displacement in the vertical direction, which can be expressed as follows:

y = yt + vyt - (1/2)gt²

where:
y = vertical displacement (final position relative to the initial position)
yt = initial vertical position (182 m, as given)
vyt = initial vertical velocity (0 m/s since the crate is dropped)
g = acceleration due to gravity (10 m/s²)
t = time

We need to find the time it takes for the crate to fall from the cargo plane to the ground. To do this, we can use another kinematic equation:

y = yt + vyt - (1/2)gt²
0 = 182 + 0 - (1/2)(10)t²
0 = 182 - 5t²
5t² = 182
t² = 182/5
t ≈ 8.544

Now that we have the time, we can substitute it back into the first equation to find the vertical displacement:

y = yt + vyt - (1/2)gt²
y = 182 + 0 - (1/2)(10)(8.544)²
y ≈ 182 - (1/2)(10)(73.031616)
y ≈ 182 - 365.15808
y ≈ -183.15808

The negative value means that the crate has fallen below the initial position. Therefore, the crate will land approximately 183.15808 m below the initial position relative to the car.

To determine the exact landing position relative to the car, we need to consider the horizontal distance between the car and the initial position of the crate. Since the crate falls directly below the initial position, the horizontal distance remains the same.

Thus, the crate will land approximately 183.15808 m below the initial position and directly below the car in the parking lot.