Question

A fox locates rodents under the snow by the slight sounds they make. The fox then leaps straight into the air and burrows its nose into the snow to catch its meal. If a fox jumps up to a height of 81 cm , calculate the speed at which the fox leaves the snow and the amount of time the fox is in the air. Ignore air resistance.

Answer 1

The speed at which the fox leaves the snow is approximately 3.987 m/s. The fox is in the air for approximately 0.407 seconds.

Step-by-step explanation:

To calculate the speed at which the fox leaves the snow, we can use the concept of vertical motion and the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. Since the fox jumps straight up, the initial velocity is 0 m/s and the displacement is 81 cm (or 0.81 m). Assuming the acceleration due to gravity is 9.8 m/s^2, we can now calculate the final velocity:

v^2 = u^2 + 2as
v^2 = 0^2 + 2(9.8)(0.81)
v^2 = 15.876
v = √15.876
v ≈ 3.987 m/s

The time the fox is in the air can be calculated using the equation v = u + at, where t is the time. Again, the initial velocity is 0 m/s and the acceleration due to gravity is 9.8 m/s^2. Plugging in these values, we have:

v = u + at
3.987 = 0 + (9.8)t
3.987 = 9.8t
t = 3.987/9.8
t ≈ 0.407 s

Answer 2

4 m/s

0.82 s

Step-by-step explanation:

h = height to which the fox jumps = 81 cm = 0.81 m

v₀ = speed at which the fox leaves the snow

v = speed of the fox at highest point = 0 m/s

a = acceleration due to gravity = - 9.8 m/s²

Using the kinematics equation

v² = v₀² + 2 a h

0² = v₀² + 2 (- 9.8) (0.81)

v₀ = 4 m/s

t = amount of time in air while going up

Using the equation

v = v₀ + a t

0 = 4 + (- 9.8) t

t = 0.41 s

T = Total time

Total time is given as

T = 2 t

T = 2 (0.41)

T = 0.82 s