A fox locates its prey under the snow by slight sounds rodents make. The fox then leaps straight into the air, and then burrows its nose into the snow to catch its meal. If a fox jumps up to a height of 75 cm, calculate (a) the speed at which the fox leaves the snow, and (b) how long the fox is in the air. Ignore air resistance.

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.