A 2.1 times 103 - kg car starts from rest at the top of a 5.0 - m - long driveway that is inclined at 20 deg with the horizontal
. If an average friction force of 4.0 times 103 N impedes the motion, find the speed of the car at the bottom of the driveway.
1 answer:
Answer:
speed of the car at the bottom of the driveway is 3.8 m/s
Explanation:
given data
mass = 2.1× 10³ kg
distance = 5 m
angle = 20 degree
average friction force = 4 × 10³ N
to find out
find the speed of the car at the bottom of the driveway
solution
we find acceleration a by force equation that is
force = mg×sin20 - friction force
ma = mg×sin20 - friction force
put here value
2100a = 2100 ( 9.8)×sin20 - 4000
a = 1.447 m/s²
so from motion of equation
v²-u² = 2as
here u is 0 by initial speed and v is velocity and a is acceleration and s is distance
v²-0 = 2(1.447)(5)
v = 3.8
speed of the car at the bottom of the driveway is 3.8 m/s
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<h2>Answer: 10.52m</h2><h2 />
First, we have to establish the <u>reference system</u>. Let's assume that the building is on the negative y-axis and that the brick was thrown at the origin (see figure attached).
According to this, the initial velocity has two components, because the brick was thrown at an angle
:
(1)
(2)
(3)
(4)
As this is a projectile motion, we have two principal equations related:
<h2>In the x-axis: </h2> (5)
Where:
is the distance where the brick landed
is the time in seconds
If we already know and
, we have to find the time (we will need it for the following equation):
(6)
(7)
(8)
Where:
is the height of the building (<u>in this case it has a negative sign because of the reference system we chose)</u>
is the acceleration due gravity
Substituting the known values, including the time we found on equation (7) in equation (8), we will find the height of the building:
(9)
(10)
Multiplying by -1 each side of the equation:
>>>>This is the height of the building