After soccer practice, Coach Miller goes to the roof of the school to retrieve the errant soccer balls. The height of the school
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Answer:
The velocity of the plane at take off is 160 m/s.
The distance travel by the plane in that time is 3200 meter.
Explanation:
Given:
Acceleration, a = 4 m/s²
Time, t = 40 s
u = 0 i .e initial velocity
To Find:
velocity , v = ?
distance , s =?
Solution:
we have first Kinematic equation
v = u + at
∴ v = 0 + 4×40
∴ v = 160 m/s
Now by Third Kinematic equation
∴ s = 0 + 0.5 × 4× 40²
∴ s = 3200 meter
Answer:
The work done by non-conservative forces on the car from the top of the first hill to the top of the second hill is 6574.75 joules.
Explanation:
By Principle of Energy Conservation and Work-Energy Theorem we present the equations that describe the situation of the roller coaster car on each top of the hill. Let consider that bottom has a height of zero meters.
From top of the first hill to the bottom
(1)
From the bottom to the top of the second hill
(2)
Where:
- Mass of the roller coaster car, in kilograms.
- Speed of the roller coaster car at the bottom between the two hills, in meters per second.
- Gravitational acceleration, in meters per square second.
- Height of the first top of the hill with respect to the bottom, in meters.
- Work done by non-conservative forces on the car between the top of the first hill and the bottom, in joules.
- Speed of the roller coaster car at the top of the second hill, in meters per seconds.
- Height of the second top of the hill with respect to the bottom, in meters.
- Work done by non-conservative forces on the car bewteen the bottom between the two hills and the top of the second hill, in joules.
By using (1) and (2), we reduce the system of equation into a sole expression:
(3)
Where is the work done by non-conservative forces on the car from the top of the first hill to the top of the second hill, in joules.
If we know that ,
,
,
and
, then the work done by non-conservative force is:
The work done by non-conservative forces on the car from the top of the first hill to the top of the second hill is 6574.75 joules.