A rescue plane is flying horizontally at a height of 132 m above the ground. The pilot spots a survivor and releases an emergency kit with a parachute. The kit descends at a constant vertical acceleration of and the initial plane horizontal speed is . Assuming air resistance and wind are negligible, how far away from the survivor will the emergency kit hit the ground?

Question

A rescue plane is flying horizontally at a height of 132 m above the ground. The pilot spots a survivor and releases an emergency kit with a parachute. The kit descends at a constant vertical acceleration of and the initial plane horizontal speed is . Assuming air resistance and wind are negligible, how far away from the survivor will the emergency kit hit the ground?

A.)301 m
B.) 2.64 km
C.) 426 m
D.) 446 m

Answer 1

A rescue plane is flying horizontally at a height of 132 m above the ground. The pilot spots a survivor and releases an emergency kit with a parachute. The kit descends at a constant vertical acceleration of and the initial plane horizontal speed is . Assuming air resistance and wind are negligible, how long will the emergency kit be falling through the air?

Answer 2

To solve this problem, we can use kinematic equations to find the horizontal distance traveled by the emergency kit before it hits the ground.

First, let's write down the known values:

Vertical acceleration (a) = unknown
Horizontal speed (v) = unknown
Initial vertical velocity (u_y) = 0 (since the kit is dropped)
Initial horizontal velocity (u_x) = unknown
Height (h) = 132 m

We can determine the vertical acceleration (a) using the formula:

h = u_yt + (1/2)at^2

Since the initial vertical velocity (u_y) is 0, the equation simplifies to:

h = (1/2)at^2

Plugging in the known values, we get:

132 = (1/2)a(t^2)

Solving for a:

a = (2h)/(t^2)

Now, let's find the time it takes for the kit to hit the ground. We can use the formula:

h = (1/2)at^2

Since the height (h) is given and the vertical acceleration (a) is unknown, we can rearrange the equation to solve for time (t):

t^2 = (2h)/a

Taking the square root of both sides, we get:

t = √[(2h)/a]

Now that we know the time (t), we can find the horizontal distance (d) traveled by the kit using the equation:

d = u_xt

Plugging in the known values, we get:

d = v * √[(2h)/a]

Comparing the given answer choices, we can calculate the respective distances for each choice and find the matching one.

Let's calculate the distances for each choice:

A.) 301 m: Not possible since the given height is 132 m.
B.) 2.64 km: Convert this to meters -> 2.64 km = 2640 m.
C.) 426 m: The calculated distance should match this value.
D.) 446 m: The calculated distance should match this value.

By using the formulas and solving for the distance, the answer options C and D are possible solutions. We can further verify by substituting the values into the equation.