<span>When the fuel of the rocket is consumed, the acceleration would be zero. However, at this phase the rocket would still be going up until all the forces of gravity would dominate and change the direction of the rocket. We need to calculate two distances, one from the ground until the point where the fuel is consumed and from that point to the point where the gravity would change the direction.
Given:
a = 86 m/s^2
t = 1.7 s
Solution:
d = vi (t) + 0.5 (a) (t^2)
d = (0) (1.7) + 0.5 (86) (1.7)^2
d = 124.27 m
vf = vi + at
vf = 0 + 86 (1.7)
vf = 146.2 m/s (velocity when the fuel is consumed completely)
Then, we calculate the time it takes until it reaches the maximum height.
vf = vi + at
0 = 146.2 + (-9.8) (t)
t = 14.92 s
Then, the second distance
d= vi (t) + 0.5 (a) (t^2)
d = 146.2 (14.92) + 0.5 (-9.8) (14.92^2)
d = 1090.53 m
Then, we determine the maximum altitude:
d1 + d2 = 124.27 m + 1090.53 m = 1214.8 m</span>
Answer
Factors Affecting Acceleration Due to Gravity
(1) Position on the planetary surface, it is higher at the axis (poles),
(2) Mass of the planet, higher with planets of larger masses
(3) Distance between object and the centre of planet, the larger the distance, the smaller the acceleration due to gravity.
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In fact, the force Rahul exerts on Earth corresponds to the force of gravity. But Rahul's weight is, in fact, the force of gravity exerted by the Earth on Rahul, and these two forces correspond to the action-reaction pair of Newton's third law, which states that the two forces are equal.
The maximum height to which the ball attain before falling back down is 1147.96 m
<h3>Data obtained from the question</h3>
The following data were obtained from the question:
- Initial velocity (u) = 150 m/s
- Final velocity (v) = 0 m/s (at maximum height)
- Acceleration due to gravity (g) = 9.8 m/s²
- Maximum height (h) =?
<h3>How to determine the maximum height </h3>
The maximum height reached by the ball can be obtained as illustrated below:
v² = u² – 2gh (since the ball is going against gravity)
0² = 150² – (2 × 9.8 × h)
0 = 22500 – 19.6h
Collect like terms
0 – 22500 = –19.6h
–22500 = –19.6h
Divide both side by –19.6
h = –22500 / –19.6
h = 1147.96 m
Thus, the maximum height reached by the ball is 1147.96 m
Learn more about motion under gravity:
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The ironwood will because it it more heavy and the others are not
The higher the amount is the more possible it is to sink
Hope this helped
