An astronaut wearing a 20-kg spacesuit jumps on the moon with an initial velocity of 16 m/s. On the moon, the acceleration due to gravity is 1.62 m/s squared. What is the maximum height he reaches?
mv²/2= mgh
h= v²/2g = 16²/2•1.62 =79 m
To find the maximum height the astronaut reaches, we need to use the equations of motion. We can assume that the upward direction is positive:
The initial vertical velocity (u) of the astronaut is 16 m/s, the acceleration due to gravity (a) is -1.62 m/s^2 (negative since it's pulling the astronaut downward), and the final vertical velocity (v) is 0 m/s at the maximum height.
To find the maximum height (h), we can use the following equation:
v^2 = u^2 + 2ah
Rearranging the equation, we get:
2ah = v^2 - u^2
Substituting the known values:
2 * (-1.62 m/s^2) * h = (0 m/s)^2 - (16 m/s)^2
Simplifying further:
-3.24 h = -256
Dividing both sides by -3.24:
h = -256 / -3.24
h ≈ 79.01 meters
Therefore, the maximum height the astronaut reaches on the moon is approximately 79.01 meters.