Answer :
The vertical launch of kinematics allows to find the flight time of the kangaroo is
t = 2.2 s
Given parameters
- Kangaroo's initial velocity vo = 36 ft / s
To find
- The time that is in the air
Vertical launch is an application of kinematics where there is no motion on the ax axis and on the y axis the acceleration is the acceleration of gravity (g = 32.16 ft / s²), the equation of motion is
y = y₀ + v₀ t - ½ g t²
The expression written in the exercise has some typing errors. Where y and y₀ are the current and initial height, respectively, v₀ the initial velocity, g the acceleration of gravity and t the time
The time of flight occurs when the kangaroo reaches the ground (y = 0)
0 = 0 + v₀ t - ½ g t²
t (v₀ - ½ g t) = 0
This expression has two solutions
t = 0 s
This solution corresponds to the time of departure and the solution for the time of arrival on the ground is
t = [tex]\frac{2v_o}{g}[/tex]
t = 2 36 / 32.16
t = 2.24 s
Using the proposed criterion of leaving a single decimal the answer is
t = 2.2 s
In conclusion with the vertical launch of kinematics we can find the flight time of the kangaroo is
t = 2.2 s
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