Q35E - University Physics with Modern Physics

Question

(a) If a flea can jump straight up to a height of 0.440 m, what is its initial speed as it leaves the ground? (b) How long is it in the air?

Step-by-Step Solution

Answer

(a) The initial speed when flea leaves the ground is u =2.94 m/s .

(b) Total time in air t = 0.3 s  

Step 1: identification of the given data

• Total distance travelled (s) =0.440 m
• Acceleration due to gravity=9.81 m/s/s.

Step 2: calculation of the initial speed

(a)

 

Final velocity is calculated by using 

$v^2=u^2+(2\times a\times s)$  

Where, v= final velocity, u=initial velocity, a=acceleration due to gravity, and s=distance travelled

 

Substituting the values,

$$\begin{gathered} {\mathrm{v}}^2={\mathrm{u}}^2+(2\times \mathrm{a}\times \mathrm{s}) \\ 0={\mathrm{u}}^2+(2\times (-9.81)\times 0.440) \\ \mathrm{u}=2.94 \mathrm{m}/\mathrm{s} \end{gathered}$$ 

  

Thus, the final velocity of the system is u =2.94 m/s.

Step 3: calculation of total time

(b)

 

The total time required is calculated by using,

$$\begin{gathered} t=\frac{u}{a} \\ t=\frac{2.94}{9.81} \\ t=0.3s \end{gathered}$$ 

  

Total time in the air is twice that as the flea has to fall to the ground again, i.e. total time in air t =0.3 s.