The minimum speed with which a projectile will travel a range is given by the speed when the given range is taken as the maximum range for the given speed
The minimum takeoff speed for such a leap is approximately 9.9 m/s
The known parameter is the distance a grey kangaroo can leap = 10 meters
The required information is the minimum takeoff speed for the leap
Solution:
The path of motion of the kangaroo as they leap is the path of a projectile
The distance of the leap is the range of the projectile
The formula for the maximum range is presented as follows;
[tex]Maximum \ range, R = \mathbf{ \dfrac{v_0^2 }{g}}[/tex]
v₀ = The initial speed of the kangaroo
g = The acceleration due to gravity ≈ 9.81 m/s²
The minimum speed to reach a maximum range of, R = 10 meters is found as follows;
[tex]\mathbf{ Maximum \ range, R} = 10 \, m = \dfrac{v_0^2 }{9.81 \ m/s^2}[/tex]
Therefore;
v₀² = 10 m × 9.81 m/s² = 98.1 m²/s²
v₀ = √(98.1 m²/s²) ≈ 9.9 m/s
The minimum takeoff speed for the kangaroo to leap 10 meters on horizontal ground, v₀ ≈ 9.9 m/s
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