An astronaut on the moon throws a wrench straight up at 4 0 m/s. Three seconds later it falls downwards at a velocity of 0.80 m/s.
What is the final velocity when the wrench leaves the astronaut's hand.
(its not 0m/s btw)
v(t) = 4.0 - gt
we have v(3) = -0.8, so
4 - 3g = -0.8
g = 1.6 m/s^2 on the moon
Not sure just what you are asking, but that's the only thing I see unanswered.
To determine the final velocity when the wrench leaves the astronaut's hand, we need to consider the upward and downward motion separately.
1. Upward motion:
The wrench is thrown straight up with an initial velocity of 40 m/s. Assuming there is no air resistance, the only force acting on it is gravity, causing it to decelerate until it reaches its highest point and starts falling. The acceleration due to gravity on the Moon is approximately 1.6 m/s^2. Using the second equation of motion (v = u + at), we can calculate the final velocity during the upward motion.
v = u + at
v = 40 m/s + (-1.6 m/s^2)(3 s)
v = 40 m/s - 4.8 m/s
v ≈ 35.2 m/s
Therefore, the final velocity during the upward motion of the wrench is approximately 35.2 m/s.
2. Downward motion:
After three seconds, the wrench starts falling back towards the Moon's surface. We are given that its velocity at this point is 0.80 m/s. Since the wrench is now moving in the opposite direction (downward), the initial velocity (u) would be negative. Using the same equation as before, we can determine the final velocity during the downward motion.
v = u + at
0.80 m/s = u + (1.6 m/s^2)(3 s)
0.80 m/s = u + 4.8 m/s
u = -4.00 m/s
Therefore, the initial velocity during the downward motion of the wrench is -4.00 m/s.
To find the final velocity when the wrench leaves the astronaut's hand, we need to sum the velocities during the upward and downward motions, as they are in opposite directions.
Final velocity = Velocity during upward motion + Velocity during downward motion
Final velocity = 35.2 m/s + (-4.00 m/s)
Final velocity ≈ 31.2 m/s
Hence, the final velocity when the wrench leaves the astronaut's hand is approximately 31.2 m/s.
To find the final velocity when the wrench leaves the astronaut's hand, we need to consider the time it takes for the wrench to travel upwards and downwards.
Given:
Initial upward velocity (when thrown) = +40 m/s
Time taken to travel upwards = 3 seconds
Final downward velocity = -0.80 m/s
Since the velocity decreases due to gravity when the wrench travels upwards, we can calculate the final velocity using the equation:
Final velocity (upwards) = Initial velocity (upwards) - (acceleration due to gravity * time taken upwards)
where acceleration due to gravity is approximately -9.8 m/s².
Final velocity (upwards) = +40 m/s - (-9.8 m/s² * 3 s) = 40 m/s + 29.4 m/s = +69.4 m/s
To find the final velocity when the wrench leaves the astronaut's hand, we consider the wrench's velocity when it starts falling downwards. Since it already starts falling with a velocity of -0.80 m/s, the final velocity will be the same.
Therefore, the final velocity when the wrench leaves the astronaut's hand is approximately -0.80 m/s.