A squirrel drops an acorn from a tree branch that is 8.0 m from the ground. How long is the acorn in the air?

What is the acorn's velocity when it reaches the ground?A squirrel drops an acorn from a tree branch that is 8.0 m from the ground. How long is the acorn in the air?
The equation would be 1/2at^2 + vt - c = 0





a = 9.81 m/s^2 (acceleration due to gravity)


v = 0 (initial velocity)


c = 8 (distance to fall)





so





1/2gt^2 = 8





(9.81 m/s^2) * t^2 = 16





t^2 = 1.63 sec^2





t = 1.28 seconds





Note: Sorry, had to correct the original questionA squirrel drops an acorn from a tree branch that is 8.0 m from the ground. How long is the acorn in the air?
F=ma


the only force is the force of gravity, so F=-mg


-mg=ma


-g=a, so in other words it accelerates downward at the acceleration due to gravity


acceleration is the second time derivative of acceleration, so: a = dy^2/dt^2





dy^2/dt^2 = -g





Integrating with respect to t, we find:


dy/dt = -gt + C1, with C1 being equal to the initial velocity, which in this case is 0, so:





dy/dt = -gt





Integrating with respect to t, we find:


y = -1/2gt^2 + C2, with C2 being equal to the initial position, so:





y = -1/2gt^2 + 8





assuming g is 9.8m/s^2:





y = -4.9t^2 + 8





the ground is at y=0, so the acorn strikes the ground at y=0, so:





4.9t^2 = 8


t=1.278s
someguy's reply is quite scientific although he overlooked one important detail: there could be a strong wind, lkie a hurrican which is actually the reason why the squirrel dropped the acorn, and therefore it could take much much longer before it touches ground...
acorn=8m. above ground


acceleration of gravity = 9.8m/s





8/9.8=0.82 seconds
18
ok well. distance is 8m. initial velocity is 0m/s and the acceleration is 9.8m/s^2.





you have to find the time and the final velocity.





first, average acceleration is v2-v1/ t


9.8 = v2 / t


v2 = 9.8t





and average velocity * time is equal to the distance


v2+v1/2 * t = d


v2/2 * t = 8


v2 * t = 16(9.8t) * t = 16


t^2 = 16 / 9.8


t = sqrt (1.63...)


t = 1.2777 seconds





v2 = 9.8 * 1.2777 = 12.52m/s
the formula used is y=(1/2)gt^2


y=height, g=acceleration on earth= (9.8m/s^2) , t=time falling


thus, 8m=(1/2)(9.8m/s^2)(t)^2


then 8m/ ((1/2)(9.8m/s^2))=t^2


so 1.63265=t^2


square root both sides, then t=1.27775
The acorn is in the air until it hits the ground.





You're welcome.