A lump of ice falls from a jet plane as it tries to land at an airport. If the ice hits the ground with a vertical speed of 85m/s, what was the height of the plane when the ice fell off.
To find the height of the plane when the ice fell off, we need to use the equations of motion in physics.
We know the final vertical speed of the ice, which is 85 m/s when it hits the ground. Let's assume the initial vertical speed of the ice when it fell off the plane is zero, as it is not given.
Using the equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity
u = initial velocity
s = displacement
a = acceleration
Since the initial speed is zero (u = 0), we can simplify the equation to:
v^2 = 2as
Plugging in the values, we have:
(85 m/s)^2 = 2 * a * s
To find the height (s) of the plane when the ice fell off, we need to find the value of 'a,' which is the acceleration due to gravity, approximately equal to 9.8 m/s^2.
(85 m/s)^2 = 2 * (9.8 m/s^2) * s
7225 m^2/s^2 = 19.6 m/s^2 * s
Simplifying the equation, we get:
s = (7225 m^2/s^2) / (19.6 m/s^2)
s = 369.9 m
Therefore, the height of the plane when the ice fell off is approximately 369.9 meters.
To calculate the height of the plane when the ice fell off, we can use the equations of motion for freefall.
Let's break down the given information:
- The vertical speed of the ice when it hits the ground is 85 m/s.
- We need to find the height of the plane when the ice fell off.
We can use the following equation of motion to solve for the height (h) of the plane:
v^2 = u^2 + 2as
Where:
- v is the final velocity (85 m/s), which is the speed at impact.
- u is the initial velocity, which is the speed of the plane.
- a is the acceleration due to gravity on Earth (approximately 9.8 m/s^2).
- s is the displacement, which is the height we need to find.
Since the ice fell off without any additional upward or downward force, we can assume that the initial vertical velocity of the ice (u) is 0 m/s. Therefore, the equation becomes:
85^2 = 0^2 + 2 * 9.8 * s
After simplifying the equation, we can solve for s (the height of the plane):
7225 = 19.6s
Dividing both sides of the equation by 19.6, we find:
s = 7225 / 19.6 ≈ 368.88
Therefore, the height of the plane when the ice fell off is approximately 368.88 meters.
since v=at and
s = 1/2 at^2,
s = 1/2 v^2/a
you know v and a, so plug and chug.