MHB Mechanics- general motion in a straight line.

Click For Summary
The discussion revolves around the motion of a ball bearing fired vertically upwards through a tub of butter, with a focus on calculating various aspects of its motion. The upward velocity is defined by the equation v=13-10t-3t^2 cm/s, and participants are asked to determine when the ball bearing comes to rest and how far it travels upwards at that point. The downward motion is described by the equation v=10T cm/s, and the challenge lies in calculating the time taken for the ball bearing to fall back to its original position after it momentarily stops. There is confusion regarding the integration process needed to solve for the time in part (c). Clarification is sought on how to correctly set up and solve the integral equation related to the downward motion.
Shah 72
MHB
Messages
274
Reaction score
0
20210608_181630.jpg

I calculated q(a)=1s
q(b)=7cm
I don't understand q(c)
 
Mathematics news on Phys.org
Fix the image to make it readable or type out the problem statement yourself.
 
skeeter said:
Fix the image to make it readable or type out the problem statement yourself.
Apologies.
A ball bearing is fired vertically upwards in a straight line through a tub of butter. The upward velocity of the ball bearing is given by v=13-10t-3t^2 cm/s, where t is the time from when it was fired upwards.
a) Find the time when the ball bearing comes momentarily to rest
b) Find how far the ball bearing has traveled upwards at this time

The ball bearing then falls downwards through the hole it has made in the butter. The downward velocity of the ball bearing is given by v= 10T cm/s, where T is the time from when it was momentarily at rest.
C) Find the time that the ball bearing takes ( from when it was momentarily at rest) to fall to its original position.
Iam not understand how to calculate (c)
 
$\displaystyle \int_0^t 10T \, dT = 7$

solve for $t$
 
skeeter said:
$\displaystyle \int_0^t 10T \, dT = 7$

solve for $t$
Thank you very much!
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB Mechanics- General motion in a straight line.
  • · Replies 7 ·
Replies
7
Views
977
MHB Mechanics- general motion in a straight line.
  • · Replies 2 ·
Replies
2
Views
1K
MHB Mechanics- general motion in a straight line.
  • · Replies 2 ·
Replies
2
Views
2K
MHB Mechanics- General motion in a straight line.
  • · Replies 4 ·
Replies
4
Views
2K
MHB General motion in a straight line.
  • · Replies 5 ·
Replies
5
Views
1K
MHB Mechanics- General motion in a straight line.
  • · Replies 6 ·
Replies
6
Views
1K
High School How Many Straight Lines to Connect an N by M Array of Points in a Closed Loop?
  • · Replies 25 ·
Replies
25
Views
3K
MHB Mechanics- General motion in a straight line.
  • · Replies 8 ·
Replies
8
Views
1K
MHB Circle a equation in a straight line
  • · Replies 8 ·
Replies
8
Views
2K
MHB What is the maximum distance of P from point O during the motion?
  • · Replies 10 ·
Replies
10
Views
2K