Answer:
t = 0.12 s
Explanation:
Applying the second equation of motion under free fall,
h = ut + [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex]
where: h is the height, u is its initial velocity, t is the time taken and g is the gravitational force.
But, u = 0 m/s, h = 21 cm (0.21 m) and g = 9.8 m/[tex]s^{2}[/tex]. Then:
0.21 = 0 + [tex]\frac{1}{2}[/tex] x 9.8 x [tex]t^{2}[/tex]
0.21 = 4.9[tex]t^{2}[/tex]
[tex]t^{2}[/tex] = [tex]\frac{0.21}{4.9}[/tex]
= 0.04286
⇒ t = 0.2070
= 0.21 s
The time taken for the flea to jump as high as 21 cm is 0.21 s.
The time taken for the flea to reach a height of 7.0 cm (0.07 m) can be determined as;
h = ut + [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex]
0.07 = 0 + [tex]\frac{1}{2}[/tex] x 9.8 x [tex]t^{2}[/tex]
0.07 = 4.9[tex]t^{2}[/tex]
[tex]t^{2}[/tex] = [tex]\frac{0.07}{4.9}[/tex]
= 0.01429
t = 0.1195
= 0.12 s
