A small first-aid kit is dropped by a rock
climber who is descending steadily at 1.6 m/s. After 1.6 s, what is the velocity of the first-aid kit? The acceleration of gravity is 9.81 m/s2.
2)How far is the kit below the climber after the
1.6 s?
vf=vi+g*t
h=vi*t+1/2 g t^2
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To find the velocity of the first-aid kit after 1.6 seconds, we need to consider the acceleration due to gravity.
1) Velocity of the first-aid kit:
The rock climber is descending steadily, which means their velocity remains constant at 1.6 m/s. Since the first-aid kit is dropped by the climber, it will also initially have the same velocity of 1.6 m/s.
Acceleration due to gravity is acting downward, which means it will cause the velocity of the first-aid kit to increase as time passes. The acceleration due to gravity is given as 9.81 m/s^2. Note that this acceleration is always acting downward.
To find the velocity after 1.6 seconds, we can use the equation of motion:
vf = vi + at
Where:
vf = final velocity
vi = initial velocity
a = acceleration
t = time
In this case,
vi = 1.6 m/s (initial velocity)
a = 9.81 m/s^2 (acceleration due to gravity)
t = 1.6 s (time)
Plugging in the values, we get:
vf = 1.6 + (9.81 * 1.6)
Simplifying this equation will give us the final velocity of the first-aid kit after 1.6 seconds.
2) Distance below the climber:
To find how far the first-aid kit is below the climber after 1.6 seconds, we can use the equation of motion:
d = vi * t + (1/2) * a * t^2
Where:
d = distance
vi = initial velocity
a = acceleration
t = time
In this case,
vi = 1.6 m/s (initial velocity)
a = 9.81 m/s^2 (acceleration due to gravity)
t = 1.6 s (time)
Plugging in the values, we get:
d = 1.6 * 1.6 + (1/2) * 9.81 * (1.6^2)
Simplifying this equation will give us the distance the first-aid kit has fallen below the climber after 1.6 seconds.
By following these steps, you should be able to find the velocity of the first-aid kit and the distance it has fallen after 1.6 seconds.