Question

If a Kangaroo jumps from the ground so that her maximum height is 2.70 m, what was the total time between jumping and landing?

a) 0.76 seconds
b) 1.96 seconds
c) 0.98 seconds
d) 2.32 seconds

Answer 1

The total time between jumping and landing for the kangaroo is approximately 0.98 seconds.The correct option is C.

Step-by-step explanation:

To calculate the total time between jumping and landing for the kangaroo, we can use the equations of motion. Firstly, we need to find the initial vertical velocity of the kangaroo when it leaves the ground.

Given that the maximum height is 2.70 m, we can calculate the final velocity using the equation: vf² = vi² + 2aΔy, where vf is the final velocity, vi is the initial velocity (which is 0 m/s as the kangaroo starts from rest), a is the acceleration (which is -9.8 m/s² for the downwards motion), and Δy is the change in height (which is 2.70 m).

Substituting the values, we have: (0 m/s)² = vi² + 2(-9.8 m/s²)(2.70 m). Solving for vi, we get vi ≈ 5.27 m/s.

Next, we can calculate the time of flight using the equation: Δy = viΔt + (1/2)a(Δt)², where Δt is the time of flight and Δy is the change in height (which is 2.70 m).

Substituting the values, we have: 2.70 m = (5.27 m/s)(Δt) + (1/2)(-9.8 m/s²)(Δt)². Rearranging the equation and solving for Δt using the quadratic formula, we find two solutions: Δt ≈ 0.43 s and Δt ≈ 0.98 s. Since the question asks for the total time between jumping and landing, we can select the longer time, which is approximately 0.98 seconds.