A rock is thrown down from the top of a cliff with a velocity of 3.61 m/s [down]. The cliff is 28.4m
above the ground. Determine the velocity of the rock just before it hits the ground.
To solve this problem, we can use the kinematic equation for final velocity:
v^2 = u^2 + 2as
Where:
v = final velocity (unknown)
u = initial velocity (3.61 m/s downwards)
a = acceleration due to gravity (9.8 m/s^2 downwards)
s = displacement (28.4 m downwards)
Plugging in the values into the equation:
v^2 = (3.61)^2 + 2(-9.8)(-28.4)
v^2 = 13.0321 + 550.24
v^2 = 563.2721
Taking the square root of both sides:
v = √563.2721
v ≈ 23.74 m/s
The velocity of the rock just before it hits the ground is approximately 23.74 m/s [downwards].
To solve this problem, we can use the kinematic equations of motion.
We are given the following information:
Initial velocity (u) = 3.61 m/s [down]
Distance traveled (s) = 28.4 m
Acceleration (a) = 9.8 m/s^2 (acceleration due to gravity, assuming downward direction as positive)
We need to find the final velocity (v) just before the rock hits the ground.
We can use the first equation of motion:
v^2 = u^2 + 2as
From the given information,
u = 3.61 m/s [down]
s = 28.4 m
a = 9.8 m/s^2
Substituting these values into the equation:
v^2 = (3.61 m/s)^2 + 2(9.8 m/s^2)(28.4 m)
Calculating:
v^2 = 13.0321 m^2/s^2 + 2(9.8 m/s^2)(28.4 m)
v^2 = 13.0321 m^2/s^2 + 558.56 m^2/s^2
v^2 = 571.5921 m^2/s^2
Taking the square root of both sides:
v = √(571.5921 m^2/s^2)
v ≈ 23.90 m/s
Therefore, the velocity of the rock just before it hits the ground is approximately 23.90 m/s [down].
To determine the velocity of the rock just before it hits the ground, we can use the equation of motion for vertical motion:
vf^2 = vi^2 + 2ad,
where:
- vf is the final velocity,
- vi is the initial velocity,
- a is the acceleration, and
- d is the displacement.
In this case, we have:
- vi = 3.61 m/s [down],
- a = acceleration due to gravity = -9.8 m/s^2 (negative sign indicates downward direction),
- d = 28.4 m.
To find the final velocity (vf), we need to solve for it using the above equation.
1. Rearrange the equation as vf^2 = vi^2 + 2ad:
vf^2 = (3.61 m/s)^2 + 2(-9.8 m/s^2)(28.4 m).
2. Calculate the values within the parentheses:
vf^2 = 13.0321 m^2/s^2 + (-554.56 m^2/s^2).
3. Add the values within parentheses:
vf^2 = -541.5279 m^2/s^2.
4. Take the square root of both sides to solve for vf:
vf = √(-541.5279 m^2/s^2).
Note: The square root of a negative value is not valid in real numbers. This implies that there is an error in our calculations or the initial information provided.
Please double-check the given values or calculations and rephrase the question if necessary.