Question

a kangaroo can jump over an object 2.81 m high.
(a) calculate its vertical speed (in m/s) when it leaves the ground.
$\boldsymbol{square}$ m/s
(b) how long (in s) is it in the air?
$\boldsymbol{square}$ s

Explanation:

Step1: Use kinematic equation for (a)

At max height, final vertical speed $v=0$. Use $v^2 = u^2 - 2gh$, solve for initial speed $u$.
$0 = u^2 - 2\times9.8\times2.81$
$u = \sqrt{2\times9.8\times2.81}$

Step2: Calculate initial vertical speed

Compute the value of $u$.
$u = \sqrt{55.076} \approx 7.42$

Step3: Find time to reach max height

Use $v = u - gt$, solve for $t_{up}$.
$0 = 7.42 - 9.8t_{up}$
$t_{up} = \frac{7.42}{9.8} \approx 0.757$

Step4: Total air time (b)

Total time is twice the time up.
$t_{total} = 2\times0.757 \approx 1.51$

Answer:

(a) 7.42 m/s
(b) 1.51 s