a worker drops a wrench from the top of a tower 90m tall. what is the velocity wgen the wrench strikes the ground?
To find the velocity of the wrench when it strikes the ground, we can use the equation of motion for vertically falling objects:
v² = u² + 2as,
where:
v is the final velocity (unknown),
u is the initial velocity (0 m/s because the wrench was dropped from rest),
a is the acceleration due to gravity (-9.8 m/s²),
and s is the distance traveled (90 m in this case, the height of the tower).
We can rearrange this equation to solve for v:
v² = 0² + 2(-9.8)(90).
v² = -1764.
Taking the square root of both sides:
v = √(-1764).
Since the velocity cannot be negative for this situation, we can discard the negative sign. Thus, the velocity of the wrench when it strikes the ground is:
v = √1764 = 42 m/s (rounded to two decimal places).
So, the velocity of the wrench when it strikes the ground is approximately 42 m/s.