Quite low
Gravitation force =
= 26.3 * 
= 2.63 *
N
Gravitation force =
A ball is thrown straight up into the air with a velocity of 12 m/s. Draw a motion diagram for the ball and then give as much qu
antitative information as you can about the motion
1 answer:
Answer:
find the diagram in the attachment.
Explanation:
Let vi = 12 m/s be the intial velocy when the ball is thrown, Δy be the displacement of the ball to a point where it starts returning down, g = 9.8 m/s^2 be the balls acceleration due to gravity.
considering the motion when the ball thrown straight up, we know that the ball will come to a stop and return downwards, so:
(vf)^2 = (vi)^2 + 2×g×Δy
vf = 0 m/s, at the highest point in the upward motion, then:
0 = (vi)^2 + 2×g×Δy
-(vi)^2 = 2×g×Δy
Δy = [-(vi)^2]/2×g
Δy = [-(-12)^2]/(2×9.8)
Δy = - 7.35 m
then from the highest point in the straight up motion, the ball will go back down and attain the speed of 12 m/s at the same level as it was first thrown
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Answer:
a) The rocket reaches a maximum height of 737.577 meters.
b) The rocket will come crashing down approximately 17.655 seconds after engine failure.
Explanation:
a) Let suppose that rocket accelerates uniformly in the two stages. First, rocket is accelerates due to engine and second, it is decelerated by gravity.
1st Stage - Engine
Given that initial velocity, acceleration and travelled distance are known, we determine final velocity (), measured in meters per second, by using this kinematic equation:
(1)
Where:
- Acceleration, measured in meters per square second.
- Travelled distance, measured in meters.
- Initial velocity, measured in meters per second.
If we know that ,
and
, the final velocity of the rocket is:
The time associated with this launch (), measured in seconds, is:
2nd Stage - Gravity
The rocket reaches its maximum height when final velocity is zero:
(2)
Where:
- Initial speed, measured in meters per second.
- Final speed, measured in meters per second.
- Gravitational acceleration, measured in meters per square second.
- Initial height, measured in meters.
- Final height, measured in meters.
If we know that ,
,
and
, then the maximum height reached by the rocket is:
The rocket reaches a maximum height of 737.577 meters.
b) The time needed for the rocket to crash down to the launch pad is determined by the following kinematic equation:
(2)
Where:
- Initial height, measured in meters.
- Final height, measured in meters.
- Initial speed, measured in meters per second.
- Gravitational acceleration, measured in meters per square second.
- Time, measured in seconds.
If we know that ,
,
and
, then the time needed by the rocket is:
Then, we solve this polynomial by Quadratic Formula:
,
Only the first root is solution that is physically reasonable. Hence, the rocket will come crashing down approximately 17.655 seconds after engine failure.