# A little help here.

1. Sep 2, 2004

### spdrxc

A ball is thrown with enough speed straight up so taht it is in teh air for several seconds. (a) What is the velocity of the ball when it gets to its highest point? (b) What is the velocity 1s before it reaches its highest point? (c) What is the change in velocity during this 1s interval? (d) What is its velocity 1s after it reaches its highest point? (e) What is the change in velocity during this 1s interval? (f) What is the change in velocity during the 2s interval? (g) What is the acceleration of the ball during any of these time intervals and at the moment the ball has zero velocity?

I am completely and utterly confused. Can someone please help me walk through this?

2. Sep 3, 2004

### pervect

Staff Emeritus
Do you know calculus at all? If you do, when f(x) is a maximum, what is the value of df/dx?

If you don't know calculus - when you throw a ball up into the air, when it reaches its peak, does it sort-of "hang there"? What is its velocity?

3. Sep 3, 2004

### tony873004

You don't need Calculus for this.

(a). What is the velocity of the ball when it gets to its highest point?
The answer is intuitive. It's at its high point for a reason. It has no more upward velocity, or it would keep going up, and that would not be it's high point. It doesn't have any downward velocity, or it would be coming from a point higher than it is now, but it is at it's highest point now. So its velocity at the top is 0.

(b). What is the velocity 1 second before it reaches it's highest point?
The rate of acceleration at Earth's surface is 9.8 meters / second / second. (Also written as 9.8 meters per second squared). That means that every second the ball's velocity changes by 9.8 meters per second. If it's travelling up, its upward velocity is slowed by 9.8 meters per second. If it's travelling down, it's downward velocity is sped up by 9.8 meters per second. If it changes by 9.8 meters every second, then it's easy to figure out how fast it was moving 1 second before it's velocity was 0.

(d). It's also easy to figure out how fast it's moving one second after it's velocity reaches 0.

Remember, velocity is not just speed, but direction. This isn't completely intuitive. If a car is driving 60 mph in a northbound direction, we say its speed or velocity is 60 mph. If the car is driving 60 mph in a southbound direction, we also say its speed or velocity is 60 mph. In everyday language, speed and velocity are used interchangebly. A person standing still on the northbound lanes of the highway would never say that a car in the southbound lanes was doing negative 60, and a car in the northbound lane was doing positive 60. He's just refer to both cars as doing 60. But in Physics, speed and velocity are not interchangeable terms. You must state the direction.

One second before the ball reaches its highest point, which direction is it moving, up or down?? And one second after reaching its highest point, which direction is it moving, up or down? This should be intuitive. Afterall, what makes the high point the high point? Remember to add this direction to your answer.

(c & e). What is the change in velocity in this one second interval? This is just a subtraction problem. You know that the ball has a velocity of 0 at the top. So if you know the velocity 1 sec before and 1 second after, subtract to get the difference. Remember to state your direction.

(f). What is the change in velocity during the 2 second interval? Pretty much the same as c & e. Just picture it in your mind. What direction is it travelling 1 sec before, and 1 sec after? And at what velocities? If you treat one as negative and the other as positive, then add or subtract them as such.

(g). What is the acceleration of the ball during any of these time intervals and at the moment the ball has zero velocity?
Hint: It's constant. It's a number used earlier in my explanation. It's a number you're going to have to get used to

I hope this helps.

Last edited: Sep 3, 2004
4. Sep 3, 2004

### spdrxc

Thanks. I was having trouble putting the concepts together, but the walkthrough was able to help me put together the missing pieces.