Question

A kangaroo can jump over an object 2.50 m high. (a) Calculate its vertical speed when it leaves the ground. (b) How long is it in the air?

Answer 1

Answer on Question #58686, Physics / Mechanics | Relativity

Question: A kangaroo can jump over an object $2.50\mathrm{m}$ high. (a) Calculate its vertical speed when it leaves the ground. (b) How long is it in the air?

Answer: a) Vertical coordinate Y depends on time:

$$y(t) = v_0 t - \frac{g}{2} t^2$$ $$v(t) = \dot{y}(t) = v_0 - g t$$

When kangaroo achieves the highest point,

$$v(t_0) = 0 \Rightarrow t_0 = \frac{v_0}{g}$$

Substitute to first equation, we obtain:

$$h = y(t_0) = v_0 t_0 - \frac{g}{2} t_0^2 = \frac{v_0^2}{2g}$$ $$v_0 = \sqrt{2 g h} = 7 m s^{-1}$$

b) Kangaroo fall down to the ground at the time $\tau$:

$$0 = y(\tau) = v_0 \tau - \frac{g}{2} \tau^2 =$$ $$\tau = \frac{2 v_0}{g} = 2 \frac{\sqrt{2 g h}}{g} = 2 \sqrt{\frac{2 h}{g}} = 1.43 s$$

Answer: a) $v_0 = 7 m s^{-1}$; b) $\tau = 1.43 s$

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