An egg falls from rest atop a 15-m tall tree. Show that it takes 1.7s for it to hit the ground below.
Daisha,
I can help you with this problem, but not with all of them. They are all pretty standard problems in a high school physics subject. Any high school physics text will give you lots of worked out examples.
Here:
One way to do it:
acceleration = -9.8 m/s^2 (gravity down)
velocity v = intial velocity + a t
so
v = 0 - 9.8 t
height = initial height + Vi t + (1/2) a t^2
so
0 = 15 + 0 t - (1/2)(9.8) t^2
so
4.9 t^2 = 15
t^2 = 3.06
t = 1.74 seconds
another way to do it:
Potential energy at 15 meters compared to on ground = m (9.8)(15) = 147 m Joules
that will be the kinetic energy at ground
(1/2) m v^2 = 147 m Joules
v^2 = 294
v = 17.15 m/s at ground
so average speed down = 17.15/2 = 8.57 m/s
15 = 8.57 t
t = 1.74 seconds again
thank you for your help. If we can't use joules and I don't know anything about the height. in this question is height and distance the same?
Yes, the distance it fell is the height, 15 meters.
To determine the time it takes for an object to fall from a certain height, we can use a physics equation called the free-fall equation. The equation is as follows:
d = 1/2 * g * t^2
Where:
d is the distance fallen (in this case, 15 m)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time taken to fall
Rearranging the equation to solve for time (t), we get:
t^2 = 2 * d / g
Substituting the values for distance (d = 15 m) and acceleration due to gravity (g = 9.8 m/s^2) into the equation, we have:
t^2 = 2 * 15 / 9.8
t^2 = 30 / 9.8
Simplifying, we find:
t^2 ≈ 3.06
To determine the value of t, we take the square root of both sides:
t ≈ √3.06
Plugging this value into a calculator, we find:
t ≈ 1.75s (rounded to two decimal places)
Therefore, it takes approximately 1.75 seconds for the egg to hit the ground below.