<span>Answer:
So it gets to the top of the ramp and stops. The parallel force pushing it down the ramp is mg sin θ, but for it to move, the frictional force must be overcome. This frictional force is μmg cos θ, where μ is the coefficient of static friction. For movement, then,
mg sin θ > μmg cos θ ==> tan θ > μ ==> θ > arctan 0.5 = 26.565° ==> θ = 27°</span>
Answer:
12.32 m/s
Explanation:
Using the formula of maximum height of a projectile,
H = u²sin²Ф/2g................... Equation 1
Where H = maximum height, u = initial velocity, Ф = angle of projection, g = acceleration due to gravity
make u the subject of the equation
u = √(2Hg/sin²Ф)............ Equation 2
Given: H = 2.3 m, Ф = 33°, g = 9.8 m/s²
Substitute into equation 2
u = √[(2×2.3×9.8)/sin²33°]
u =√ [45.08/(0.545)²]
u = 45.08/0.297
u = √(151.785)
u = 12.32 m/s
Answer: 0.55 m/s
Explanation:
This situation is related to projectile motion (also called parabolic motion), where the main equations are as follows:
(1)
(2)
Where:
is the horizontal displacement of the pencil
is the pencil's initial velocity
since we are told the pencil rolls <u>horizontally</u> before falling
is the time since the pencil falls until it hits the ground
is the initial height of the pencil
is the final height of the pencil (when it finally hits the ground)
is the acceleration due gravity, always acting vertically downwards
Begining with (1):
(3)
(4)
Finding
from (2):
(5)
(6)
Substituting (6) in (4):
(7)
Isolating
:
(8)
(9)
Finally:
Answer:
it states that energy can neither be created or destroyed
The car traverses a distance
after time
according to

where
is its acceleration, 10 m/s^2. The time it takes for the car to travel 25 m is

5 is pretty close to 4, so we can approximate the square root of 5 by 2. Then the car's velocity
after 2 s of travel is given by

which makes C the most likely answer.