Given: h = 75cm = 0.75 m
Find: vi, t
The equations we can use are:
v = vi - 9.81 t
y = vi t - 4.905 t²
There's an additional piece of information that we know. At
the peak of the jump, when the fox is at height h, it has zero velocity:
0 = vi - 9.81 tp
0.75 = vi tp - 4.905 tp²
We are now left with two equations and two unknowns. We can
solve for vi, the initial velocity.
vi = 9.81 tp
0.75 = 9.81 tp² - 4.905 tp²
0.75 = 4.905 tp²
tp = 0.391 seconds
vi = 9.81 tp = 3.84 m/s
That's one answer. Using the second equation again:
y = vi t - 4.905 t²
0 = 3.84 t - 4.905 t²
0 = t (3.84 - 4.905 t)
t = 0, 0.783 s
So the fox leaves the snow at 3.84 m/s, and spends 0.783
seconds in the air.
