Asked by SYAKIRAH
How High?- No Air Resistance
Suppose a small cannonball weighing 16 pounds is shot vertically upward, as shown in Figure 1, with an initial velocity v0 = 300 ft/s. The answer to the question “How high does the cannonball go?” depends on whether we take air resistance into account.
a) Suppose air resistance is ignored. If the positive direction is upward, then a model for the state of the cannonball is given by md2s/dt2 = -mg or d2s/dt2 = -g, where g is the force of the gravity. Take g = 32ft/s2, find the velocity v(t) of the cannonball at time t.
b) Use the result obtained in part (a) to determine the height s(t) of the cannonball measured from ground level. Find the maximum height attained by the cannonball.
Suppose a small cannonball weighing 16 pounds is shot vertically upward, as shown in Figure 1, with an initial velocity v0 = 300 ft/s. The answer to the question “How high does the cannonball go?” depends on whether we take air resistance into account.
a) Suppose air resistance is ignored. If the positive direction is upward, then a model for the state of the cannonball is given by md2s/dt2 = -mg or d2s/dt2 = -g, where g is the force of the gravity. Take g = 32ft/s2, find the velocity v(t) of the cannonball at time t.
b) Use the result obtained in part (a) to determine the height s(t) of the cannonball measured from ground level. Find the maximum height attained by the cannonball.
Answers
Answered by
oobleck
If you plug in your numbers you will get a model of the form
h(t) = at^2 + bt + c
As with all such parabolas, the vertex is at (-b/2a, c - b^2/4a)
h(t) = at^2 + bt + c
As with all such parabolas, the vertex is at (-b/2a, c - b^2/4a)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.