A mass is dropped from a height of 30m, and at the same time from ground level (and directly beneath the dropped mass), and another mass is thrown straight up with a speed of 15 m/s.
a) How far apart are the two masses after 0.5 s?
b) Will the massses ever meet or pass each other? And if so will the meeting place take place while both masses are falling or when one is falling and the other is rising?
a)
y=Yo + Vo time + 1/2 a time^2
0 = 30+0t =1/2 (-9.8)t^2
0=30 + 1/2 (-9.8)t^2
t^2 = -30/(-9.8* 2)
t=1.237 seconds
y=Yo + Vo time + 1/2 a time^2
0 =0 + (15m/s)t +1/2 (-9.8)t^2
t=3.06122 seconds
Did I do this correctly?
Then how will i figure out how far apart the two masses are after .5 seconds? Also How can I figure out part b?
A mass is dropped from a height of 30m, and at the same time from ground level (and directly beneath the dropped mass), and another mass is thrown straight up with a speed of 15 m/s.
a) How far apart are the two masses after 0.5 s?
b) Will the massses ever meet or pass each other? And if so will the meeting place take place while both masses are falling or when one is falling and the other is rising?
for a: I don't understand how you set y to zero. Y is what you are solving for at t=.5 sec. So solve for y at that time for each ball, and see where they are. The difference between those y is how far apart they are.
for b: set each y equation equal to the other, and solve for time.
30 +1/2 (-9.8)t^2 = (15)t +1/2(-9.8)t^2
a) I got 8.725 for the ball dropped. I got 6.275 for the ball thrown up .
So 2.45 would be how far apart they are?
b)30 +1/2 (-9.8)t^2 = (15)t +1/2(-9.8)t^2
30 + -4.9t^2 = 15t + -4.9t^2
30=15t +o
t= 2s
Are these correct?
a/ I didn't check the math, but yes, the difference in the y's is how far apart they are. Isnt the unit meters?
b. at t=2 they meet.
a) Yes, you calculated correctly. The distance between the two masses after 0.5 s is 2.45 meters.
b) However, your calculation for part b is incorrect. When setting the two y equations equal to each other, you made a mistake in simplifying.
The correct equation should be: 30 + 1/2 (-9.8)t^2 = 0 + 15t + 1/2 (-9.8)t^2.
By canceling out the common terms on both sides of the equation, we get:
30 = 15t.
Simplifying further, we find:
t = 2 seconds.
So, the masses will meet or pass each other after 2 seconds. Since one mass is falling and the other is rising, the meeting place will occur when one is falling and the other is rising.