An astronaut on a different planet can jump a distance of 19.0 meters if her initial speed is 2.60 m/s?

Question

What is the free-fall acceleration on the planet?

Answer 1

x = (Vf^2- Vo^2)/2a + Xo

19 = (0 - 2.6^2)/2a + 0

19 = -6.76/2a

2a = -6.76/19 = -.35578

a = -.17789 m/s^2, negative because its downwards

Answer 2

The potential energy in a gravitational field with acceleration a is m*a*h. When the max hp is reached, the potential energy is equal to the initial kinetic energy, .5*m*v0^2. Therefore hp*a*m = .5*m*v0^2, or a = (.5*v0^2)hp.

An alternate method: hhe height reached is given by the equation h = v0*tp - .5*a*tp^2, where tp is the time it takes to reach the top. The velocity is v = v0-a*t. At the top of the jump, v = 0, so v0=a*tp. In the equation for h, multiply both sides by a: a*hp = v0*a*tp - .5a^2*tp^2. plug in v0 for a*tp to get a*hp = v0^2 - .5*v0^2 = .5v0^2, Therefore a=(.5*v0^2)/hp.