SOLUTION: At a baseball game, the batter hits the baseball straight up at an initial velocity of +42m/s. A) at what time will the ball reach its highest point b) what will be the maximum

Question 1163928: At a baseball game, the batter hits the baseball straight up at an initial velocity of +42m/s.
A) at what time will the ball reach its highest point
b) what will be the maximum height the ball reaches
BTW the answer is about 4.3 secs for part a and 90 m for part b.. could you pls show me the steps i need its for my hw. THANKS!!
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Using the mks measurement system, the function that describes the height of a projectile where the gravitational acceleration constant is at time with an initial vertical velocity component magnitude of and an initial height of is:

For objects near the earth's surface,

Since you don't specify the height of the ball when the bat impacted it, we have to assume

That makes your function:

This would graph as a concave down parabola because the lead coefficient is negative. The answer to part a) is the value of at the vertex of the parabola. The answer to part b) is the value of the function at the answer to part a.

If you have a parabola described by:

The -coordinate of the vertex is given by

The value of the function at the vertex is then:

4.3 seconds is close enough for part a, but part b is inaccurate by an amount equal to the actual height of the ball when the bat hit it. The bat certainly wasn't on the ground if the batter hit a pop-up. So, that bat had to be a meter to a meter and a half off of the ground -- perhaps more, and the real world answer to part b would be somewhere in the range of 91 to 92 meters.

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52887)   (Show Source): You can put this solution on YOUR website!
.

In this site, there is a bunch of lessons on a projectile thrown/shot/launched vertically up
    - Problem on a projectile moving vertically up and down
    - Problem on an arrow shot vertically upward
    - Problem on a ball thrown vertically up from the top of a tower
    - Problem on a toy rocket launched vertically up from a tall platform

Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
Read them attentively and learn how to solve this type of problems once and for all.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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