A lump of ice falls from an airplane as it comes it to land. If the ice hits the ground with a vertical speed of 85 m/s, what was the height of the plane when ice feel off?
To find the height of the plane when the ice fell off, we can use the equations of motion. We'll need to know the time it takes for the ice to hit the ground.
Let's assume the initial velocity of the ice is zero as it falls from the plane.
Using the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (vertical speed of the ice when it hits the ground) = -85 m/s (negative sign represents downward direction)
u = initial velocity = 0 m/s
a = acceleration due to gravity ≈ -9.8 m/s^2 (negative sign represents downward acceleration)
s = displacement or height of the plane when the ice fell off (what we need to find)
Plugging in the values, we get:
(-85)^2 = (0)^2 + 2(-9.8)s
7225 = -19.6s
Dividing both sides by -19.6, we can solve for s:
s = 7225 / -19.6
s ≈ -368.88 meters
The negative sign indicates that the height of the plane when the ice fell off was 368.88 meters below the ground.
To find the height of the plane when the ice fell off, we need to understand the concept of free fall and solve a kinematic equation.
First, we know that the initial vertical velocity of the ice (v₀) when it fell off the plane is 85 m/s. We need to find the height (h) of the plane.
In free fall, an object accelerates downwards due to gravity at a constant rate of 9.8 m/s². We can now use the kinematic equation:
v² = v₀² + 2ah
Where:
v = final velocity (0 m/s since the ice hit the ground)
v₀ = initial velocity (85 m/s downwards)
a = acceleration (-9.8 m/s² downwards)
h = height of the plane
Substituting the known values into the equation:
0² = (85 m/s)² + 2(-9.8 m/s²)h
Simplifying, we get:
0 = 7225 - 19.6h
Rearranging the equation:
19.6h = 7225
Dividing both sides by 19.6:
h ≈ 369.9 meters
Therefore, the height of the plane when the ice fell off is approximately 369.9 meters.
vf^2=2*g*height
solve for height