Question 1151156
<font face="times" color="black" size="3">
For the planet Mars, g = 3.7 m/s^2 is the acceleration of gravity. 
d = 100 is the starting height in meters.
h = 25 is the ending height we want the object to be at (ie the object travels 100-25 = 75 vertical meters through the air)


We will plug those values into the equation and solve for t
h = -0.5*t^2*g + d
25 = -0.5*t^2*3.7 + 100
25 = -0.5*3.7*t^2 + 100
25 = -1.85t^2 + 100
25 + 1.85t^2 = 100
1.85t^2 = 100-25
1.85t^2 = 75
t^2 = 75/1.85
t^2 = 40.5405405405405
t = sqrt(40.5405405405405)
t = 6.36714539967013
t = 6.4
When starting at a height of 100 m, it takes <font color=red size=4>approximately 6.4 seconds</font> for the object to fall to a height of 25 meters. In other words, it takes roughly 6.4 seconds for the object to fall 75 meters when starting at a height of 100 meters. This only applies on the planet Mars.


-----------------------------------------------------------------------


For Venus, repeat the same basic steps as in the previous part above. The only difference is that g = 8.9 (bigger planet means stronger gravitational pull). 
The other values d = 100 and h = 25 remain the same.


h = -0.5*t^2*g + d
25 = -0.5*t^2*8.9 + 100
25 = -0.5*8.9*t^2 + 100
25 = -4.45t^2 + 100
25 + 4.45t^2 = 100
4.45t^2 = 100-25
4.45t^2 = 75
t^2 = 75/4.45
t^2 = 16.8539325842697
t = sqrt(16.8539325842697)
t = 4.1053541362798
t = 4.1

When starting at a height of 100 m, it takes <font color=red size=4>approximately 4.1 seconds</font> for the object to fall to a height of 25 meters on the planet Venus.


For each planet, we are ignoring air resistance because that greatly complicates the problem. 
</font>