If a bug can jump in the air to a height of 23.0 cm whats the initial speed as it leaves the ground?

Question

Thanks in advance... I tried using the equation y=vt + 1/2at^2 but I think rearranging the equation is not something I'm doing right.

Answer 1

assuming no air resistance, us ethe equation
v(t)=v0-g*t
and
y(t)=v0*t-.5*g*t^2

at the max height, v(t)=0
so
v0=g*t
plug into y(t)
0.23=g*t^2-.5*g*t^2
solve for t, and then multiply by g to get v0
t=sqrt(0.23*2/g)

v0=sqrt(g*0.23*2)

j