Ahuman expedition lands on an alien planet. one of the explorers is able to jump a maximum distance of 14.5 m with an initial speed of 2.50 m/s. find the gravitational acceleration on the surface of the alien planet. assume the planet has a negligible atmosphere. (enter the magnitude in m/s2.)

0.215

Explanation:

by using the  equations of the constant acceleration motion or uniformly accelerated rectilinear motion:

V= + a⋅t  

X=+ *t +

in this case = 0, = 2.5 and X= 14.5.

replacing those numbers in the equations,and knowing that a gravitational acceleration is always negative :

1.   V= 2.5 - a⋅t

2.   14.5=2.5 *t -

we have 2 unknowns (g and t) ,so this can be solve by the Substitution Method :

0= 2.5 - a⋅t  

V in this case will be 0,because the speed at the maximum distance is 0.

by solving for a:

3.   a=

and replacing in 2. :

14.5=2.5 *t -

14.5=2.5 *t -

14.5=

by solving for t:

t =  

t= 11.6 s

with this value of t,replacing in 3.  :

a=

a= 0.215