The answers would be the following:
a.) 79.38 m/s
b.) 321.49 m
You might need the solution so here you go:
First things first, you need to understand that this is a free fall motion. Everything no matter the mass is pulled by gravity at the same acceleration of 9.8 m/s² so the given mass will not be needed to solve for the answers:
Here's what we know or was given by the problem:
t = 8.1 s
a = 9.8m/s² (This is constant, because only gravity is acting upon the acorn)
Vi = 0 m/s
For the two problems you will need the following formulas:
a.) [tex]V_{f} = V_{i} + at[/tex]
b. [tex]d = Vi + \frac{1}{2}at^{2}[/tex]
Where:
Vf is the final velocity, before it hits the ground.
Vi is the initial velocity, which is 0 m/s because it was not moving till it fell.
a is the acceleration due to gravity
t is time
d is displacement
Now all you have to do is plug in what you know and solve for what you don't know:
A.
[tex]V_{f} = V_{i} + at[/tex]
[tex]V_{f} = 0m/s+(9.8m/s^{2})(8.1s)[/tex]
[tex]V_{f} =(9.8m/s^{2})(8.1s)[/tex]
[tex]V_{f} =79.38m/s[/tex]
B.
[tex]d = V_{i} + \frac{1}{2}at^{2}[/tex]
[tex]d = 0 m/s + (\frac{1}{2})(9.8m/s^{2})(8.1s)^{2})[/tex]
[tex]d = (4.9m/s^{2})(65.61s^{2})[/tex]
[tex]d = 321.49m[/tex]
