From her bedroom window a women drops a

Answered question

2022-05-08

From her bedroom window a women drops a set of keys to the ground 9m below.The keys are released from rest….how long are the keys in the air

 

Find the speed of keys as they hit the ground

Answer & Explanation

Jazz Frenia

Jazz Frenia

Skilled2023-05-05Added 106 answers

We are given that a woman drops a set of keys from her bedroom window to the ground, which is a distance of 9m below. The keys are released from rest, and we need to find how long they are in the air and the speed at which they hit the ground.
To solve this problem, we can use the kinematic equations of motion. Since the keys are dropped from rest, their initial velocity is zero. We can use the equation
y=y0+v0t+12at2,
where y is the final position of the keys, y0 is the initial position (which is 0), v0 is the initial velocity (which is 0), a is the acceleration due to gravity (which is 9.8 m/s2), and t is the time the keys are in the air.
Solving for t, we get
y=y0+v0t+12at2
9 m=0+0·t+12(9.8 m/s2)t2
t=2(9 m)9.8 m/s2
1.42 s.
Therefore, the keys are in the air for about 1.42 seconds.
To find the speed of the keys when they hit the ground, we can use the equation
v=v0+at,
where v is the final velocity, v0 is the initial velocity (which is 0), a is the acceleration due to gravity (which is 9.8 m/s2), and t is the time the keys are in the air.
Solving for v, we get
v=v0+at
=0+(9.8 m/s2)(1.42 s)
13.92 m/s.
The negative sign indicates that the velocity is directed downwards. Therefore, the speed of the keys when they hit the ground is about 13.92 meters per second.

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