At what point in its trajectory does a batted baseball have its minimum speed?

Question

1. at the end point
2. at the beginning point
3. at the top
4. somewhere at the middle height

Answer 1

It depends on what assumptions you make.
If the ball can be assumed to change direction by 180 degrees when struck by at bat then there must be a point while being struck at which it has zero speed, by definition this must be a minimum speed.

A similar argument could also be applied at the other end if the ball is caught (again there must be a zero speed point).

If we ignore the limiting points at the ends then it depends on what assumption is made about air resistance. It this is ignored (or assumed to be negligible), then the minimum speed is at the top of the trajectory. This can be seen because energy is conserved and if no energy is lost to friction (air resistance) then the ball only interchanges energy between kinetic and potential energies, potential energy is maximum at the highest point, so kinetic energy - and hence speed - must be lowest at this point.

If air resistance is added then energy is continuously lost throughout the flight so the minimum speed would be at some point after (probably only just after) the highest point.

Answer 2

3

Answer 3

3

Answer 4

Baseball Q: relies upon on the trajectory, preliminary translational velocity and angular velocity. in simple terms vertical upwards preliminary velocity with out spin, the backside velocity is unquestionably on the precise, that's 0. If the ball is flung with spin such that it has raise upwards or in the different path and is thrown horizontally or with a horizontal element, the backside velocity will ensue sometime in the process the flight (because it is going to benefit some potential because of vertical acceleration) which could't be easily desperate. The question is below constrained to furnish you a very valid answer because it needs to remark on what variety of trajectory the ball is taking. on your 2nd question, artwork out the time taken for the gadgets to fall 5.2m (it will be the comparable because of the fact you're ignoring air resistance). Use this time and the preliminary velocity to artwork out horizontal distance coated in that factor (you're assuming the backside of the water fall is somewhat horizontal and 5.2m below the precise of the waterfall right here).

Answer 5

Nice question....

The balls trajectory can be divided into a x (distance) and y( height) component. The y velocity is lowest at the top of the trajectory. The x velocity is zero at the end point. So I'm afraid it all depends on the angle the ball is struck.

Answer 6

it was batted upwards-ish?

if it's a frictionless baseball, at the top. In real life, somewhere before the top.

if it was batted horizontally and it's frictionless, the minimum speed is at the moment it's batted (the rest is acceleration towards earth). If it's not frictionless, you can't say when the minimum speed will be.

pedants will argue that the baseball has its minimum speed when it's landed in some guy's supersized coke, but I say that's cheating.

Answer 7

3.
Assuming no air resistance, the horizontal velocity is always the same and at the top, the vertical velocity is zero.

In real life where there is air resistance, the horizontal velocity will slow down as time goes by, and the vertical velocity is zero.

Answer 8

At the top - it has no vertical velocity then, only horizontal.

Answer 9

At the apex - - (the middle or top)

Answer 10

at the top