A climber descends down a vertical cliff using a rope. If they have a constant downward acceleration of 2 m/s² due to gravity, calculate the time it takes for the climber to reach the ground if they start from rest.
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We can use the equation of motion for an object undergoing constant acceleration to solve this problem:
v = u + at
where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is the time
In this case, the climber starts from rest, so the initial velocity (u) is 0 m/s. The acceleration (a) is given as 2 m/s². We need to find the time (t) it takes for the climber to reach the ground, so the final velocity (v) is also unknown.
To find v, we can use the equation:
v² = u² + 2as
where:
- s is the vertical displacement
- v is the final velocity
- u is the initial velocity
- a is the acceleration
In this case, since the climber is descending downwards, s is negative. The final velocity (v) at the ground will also be 0 m/s (since the climber comes to rest).
Therefore, the equation becomes:
0² = 0² + 2(-2)s
0 = -4s
s = 0
The climber will reach the ground (i.e., the vertical displacement, s) when s = 0. Plugging this value into the equation of motion, we can solve for t:
0 = 0 + 2(-2)t
0 = -4t
t = 0
Therefore, the time it takes for the climber to reach the ground is 0 seconds.
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