Please help me with the set up and solutions (algebra based physics) A large bou
ID: 1706164 • Letter: P
Question
Please help me with the set up and solutions (algebra based physics)A large boulder is ejected vertically upward from a volcano with an initial speed of 40.7 m/s. Air resistance may be ignored. 1)at what time after being ejected is the boulder moving at a speed 19.8 m/s upward? 2)At what time is it moving at a speed 19.8m/s downward? 3)When is the displacement of the boulder from its initial position zero? 4)When is the velocity of the boulder zero? 5)What is the magnitude of the acceleration while the boulder is moving? 6)What is the direction of the acceleration while the boulder is moving?
Explanation / Answer
supplement to last post, adding more explanations
there are two equations used here for one dimensional motion under constant acceleration
(A) v(t) = v(0) + at
(B) y(t) = v(0)t + (1/2)at^2
when applied to this case, we assign positive direction upward.
1) v = v0 - gt (this is from equation A)
rearrange to solve for t yields t = (v0-v) / g = (40.7-19.8)/9.8 = 2.13 s
2) t = (v0 -v)/g = (40.7-(-19.8))/9.8 = 6.17 s ( same equation as in (1), but notice that the velocity is negative because it is downward now)
3) y = v0t -1/2 gt^2 = 0 ( this is from equation B)
rearrange to solve for t yields t = 2v0/g = 2 * 40.7 / 9.8 = 8.30 s
4) 0 = v0 - gt (from equation A)
t = v0/g = 40.7 /9.8 = 4.15 s
5) 9.8 m/s^2, gravity is the only force acting on the boulder, gravitational acceleration is 9.8 m/s^2
6) down. gravitational acceleration is always downward.