An astronaut jumps on the moon with an initial upward velocity of 4.35m/s. If the acceleration of gravity on the moon is -1.62m/s^2, what is the max height of the astronaut?
To find the maximum height reached by the astronaut on the moon, we can use the kinematic equation for vertical motion:
vf^2 = vi^2 + 2ad
Where:
vf is the final velocity (which is 0 at the highest point),
vi is the initial velocity,
a is the acceleration (which is the acceleration due to gravity on the moon, -1.62 m/s^2),
and d is the displacement (which is the maximum height reached).
Plugging in the given values:
0 = (4.35 m/s)^2 + 2*(-1.62 m/s^2)*d
Simplifying the equation:
0 = 18.9225 m^2/s^2 - 3.24 m/s^2 * d
Rearranging the equation:
3.24 m/s^2 * d = 18.9225 m^2/s^2
Dividing both sides by 3.24 m/s^2:
d = 18.9225 m^2/s^2 / 3.24 m/s^2
Calculating the value:
d ≈ 5.83 meters
Therefore, the maximum height reached by the astronaut is approximately 5.83 meters.
To find the maximum height reached by the astronaut, we can use the kinematic equation that relates displacement, initial velocity, acceleration, and time. The equation we'll use is:
vf^2 = vi^2 + 2ad
Where:
vf is the final velocity (which will be 0 at the maximum height since the astronaut momentarily stops)
vi is the initial velocity (4.35m/s, but in the opposite direction since it's upwards)
a is the acceleration (-1.62m/s^2)
d is the displacement (the maximum height, which we want to find)
Rearranging the equation, we have:
d = (vf^2 - vi^2) / (2a)
We can substitute the known values into the equation:
d = (0 - (4.35)^2) / (2 * -1.62)
Calculating the expression in the parentheses first:
d = (-18.9225) / (2 * -1.62)
Now, simplify the expression further:
d = 18.9225 / 3.24
Finally, compute the division:
d ≈ 5.83 meters
Therefore, the maximum height reached by the astronaut is approximately 5.83 meters on the moon.
Vo = 4.35 m/s.
g = -1.62 m/s^2
V^2 = Vo^2 + 2g*h. = 0 @ h max.
h = -(Vo^2)/2g