# Basic Kinematic Problem

1. Mar 5, 2012

### mtsac

I understand many of you may take me for a fool since this is a practically elementary physics problem but I really need some help finding out the right formulas or formula to solve it. No answers though, I actually want to learn this stuff.

Problem:
You shoot an arrow into the air. After 1.2 seconds the arrow has gone straight upward to a height of 32.0 m above its launch point. Ignore air resistance.

(a) What was the arrow's initial speed?
(b) How long did it take for the arrow to first reach a height of 16 m above its launch point?

So far, the variables I have are as following:

Δx= 32m
Δt= 1.2s
(pretty obvious)

I calculated the average velocity to be 26.66m/s using the formula v=Δx/Δt. Thus,making the final velocity 53.33m/s? Yes/no? For acceleration, I got 5.53m/s^2, but it just doesn't add up.

Above all else, I find the initial speed question particularly confusing. Can one not assume that the arrow began with an initial speed of 0m/s since it was in a resting state? Or is one supposed to assume the initial speed is the speed the arrow reaches almost instantaneously after it is launched?

I'd greatly appreciate any help.
Thank you

2. Mar 5, 2012

### seekingtuva

I would suggest going to https://www.physicsforums.com/showthread.php?t=110015 and looking at the equations in the first section, 1D Kinematics. The acceleration here is acceleration due to gravity, so that velocity is decreasing at 9.81 m/s each second as the arrow travels upwards, reaching an instantaneous velocity of zero at its highest point, and then increases by 9.81 m/s each second as it falls.

So, if you want to deal with the arrow's upward journey only, its initial velocity is unknown, but its final velocity is zero. This initial velocity you are seeking is the velocity at the instant of launch, for, as you say, the arrow is at rest with respect to the bow just before this.

Hope this helps ... don't be self-conscious. Physics is beautiful, and even the best had to muddle through one-dimensional motion at some point. I still do lots of muddling.

3. Mar 5, 2012

### e^(i Pi)+1=0

Don't forget that the acceleration is negative.