An orange of mass 40g falls freely from a tree to the ground through a distance of 2.5m. Calculate the velocity just before it hits the ground.
Velocity = speed/time
I have no speed or time so what do I do.
potential energy (gravitational) = m*g*h
Kinetic energy (motion) = 1/2 * m*v^2
before the orange was dropped from the tree:
KE_inital = 1/2 * m * v_i^2 = 0
(because it's a rest, no velocity)
PE_initial = m*g*h_i
= 40g * 9.81m/s^2 * 2.5 = 981kJ
Before its the ground:
PE_final = m*g*h_f = 0
(because h is just about 0)
KE_final = 1/2 * m * v_f^2
From the conservation of energy law:
KE_inital+PE_inital = KE_final + PE_final
0 + 981 = 1/2*m*v_f^2 + 0
981 = 1/2 * m * v_f^2
solve for v_f
You can also use newton's equations of motion, it's the same concept:
http://www.physicsclassroom.com/calcpad/newtlaws
v_f^2 = v_o^2 +2*a*d
a=acceleration=gravity=9.81 m/s^2
d=distance=2.5 m
v_o = initial velocity = 0 (at rest)
To calculate the velocity of the orange just before it hits the ground, you can make use of the laws of motion. Specifically, we can use the equation of motion:
Final velocity squared = Initial velocity squared + 2 * acceleration * distance
In this case, the orange is falling freely under the influence of gravity, which means the acceleration is equal to the acceleration due to gravity (9.8 m/s^2).
First, convert the mass of the orange from grams to kilograms:
mass = 40g = 0.040kg
Next, we can rearrange the equation to solve for the final velocity:
Final velocity = √(Initial velocity squared + 2 * acceleration * distance)
Since the orange starts from rest (initial velocity = 0 m/s), the equation simplifies to:
Final velocity = √(2 * acceleration * distance)
Now we can substitute in the known values:
Final velocity = √(2 * 9.8 m/s^2 * 2.5 m)
Final velocity = √(49 m^2/s^2)
Final velocity = 7 m/s
Therefore, the velocity of the orange just before it hits the ground is approximately 7 m/s.