If an automobile had a 100%-efficient engine, transferring all of the fuel's energy to work, would the engine be warm to your to
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Answer:
v =
Explanation:
For this exercise we must use the projectile launch ratios, let's start by finding the time it takes to reach the bottom of the cliff, the initial vertical velocity is zero
y = y₀ + t - ½ g t²
at the bottom of the cliff y = 0 and as the body is thrown horizontally the initial vertical velocity is zero
0 = y₀ + 0 - ½ g t²
t =
this time is the same as the horizontal movement.
Let's use Newton's second law to find the acceleration on this x-axis due to the force of the air
F = m aₓ
they tell us that force is equal to the weight of the body
-mg = maₓ
aₓ = -g
the sign indicates that the acceleration is to the left
we write the kinematics equation
x = x₀ + v₀ₓ t + ½ aₓ t²
They indicate that the final position is the foot of the cliff (x = 0), when it leaves the top it is at x₀ = 0 and has a velocity v₀ₓ = v
we substitute
0 = 0 + v t + ½ (-g) t²
v = ½ g t
we use the drop time
v = ½ g
v =
The stone's acceleration, velocity, and position vectors at time are
where
and is the height of the building and initial height of the rock.
(a) After 6.1 s, the stone has a height of 5 m. Set the vertical component of the position vector to 5 m and solve for
:
(b) Evaluate the horizontal component of the position vector when
:
(c) The rock's velocity vector has a constant horizontal component, so that
where
For the vertical component, recall the formula,
where and
are the initial and final velocities,
is the acceleration, and
is the change in height.
When the rock hits the ground, it will have height . It's thrown from a height of
, so
. The rock is effectively in freefall, so
. Solve for
:
(where we took the negative square root because we know that points in the downward direction)
So at the moment the rock hits the ground, its velocity vector is
which has a magnitude of
(d) The acceleration vector stays constant throughout, so