Question

A kangaroo can jump over an object 2.46 m high. (a) Calculate its vertical speed (in m/s) when it leaves the ground.

m/s
(b) How long (in s) is it in the air?

Answer 1

a) 6.95 m/s

b) 1.42 seconds

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.81 m/s²

`v^2-u^2=2as\\\Rightarrow -u^2=2as-v^2\\\Rightarrow -u^2=2* -9.81* 2.46-0^2\\\Rightarrow u=√(2* 9.81* 2.46)\\\Rightarrow u=6.95\ m/s`

a) The vertical speed when it leaves the ground. is 6.95 m/s

`v=u+at\\\Rightarrow t=(v-u)/(a)\\\Rightarrow t=(0-6.95)/(-9.81)\\\Rightarrow t=0.71\ s`

Time taken to reach the maximum height is 0.71 seconds

`s=ut+(1)/(2)at^2\\\Rightarrow 2.46=0t+(1)/(2)* 9.81* t^2\\\Rightarrow t=\sqrt{(2.46* 2)/(9.81)}\\\Rightarrow t=0.71\ s`

Time taken to reach the ground from the maximum height is 0.71 seconds

b) Time it stayed in the air is 0.71+0.71 = 1.42 seconds