Question

A grey kangaroo can lead a distance of 10m on horizontal ground. what is the minimum takeoff speed for such a leap?

Answer 1

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;

$Maximum \ range, R = \mathbf{ \dfrac{v_0^2 }{g}}$

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;

$\mathbf{ Maximum \ range, R} = 10 \, m = \dfrac{v_0^2 }{9.81 \ m/s^2}$

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

Learn more about projectile motion here:

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