# Finding Final Velocity & Displacement

• golbez22
In summary: The horizontal co-ordinate is 120.5m, so you need to add 15m to the vertical co-ordinate to get the final position of the arrow. In summary, the arrow will be 120.5m from the origin, at a height of 15m.

## Homework Statement

A man shoots an arrow 145m/s at 61o from a height of 15m where the ground below is the origin.

A.) Where will the arrow be in 1.5 seconds (X,Y)?
B.) What will be the displacement when the arrow lands in regards to where it was shot from

## Homework Equations

I believe the kinematic equation Displacement=Vit+(1/2a)t2

X=ViCosTheta
Y=ViSinTheta
Theta=Tan-1(Y/X)

as well as Vf=Vi-at

where
Vi = Initial Velocity
Vf = Final Velocity
a = Acceleration
t = Time

## The Attempt at a Solution

I got 105.4m for x and 190 - 1.5(9.83) for y

for my location of where the arrow landed I got (1050m,-15m), because -15 is (0,0) and in regards to where it was shot it is 15m down and 1050=145*12.8+(1/2 -9.83)*12.82

for the Vf I got 19.1m/s because Vf=145-9.83*12.8

Note: I honestly am lost how to solve the problems

I got 105.4m for x and 190 - 1.5(9.83) for y

I get same answer for x.

The answer for y is wrong. It looks like you got the vertical component of the initial velocity right (but the last bit is wrong). The SUVAT equation you used I know as...

S = ut + 0.5at2

S = displacement
u = Initial Velocity
a = acceleration
t = time

= 145Sin(61)1.5 + 0.5(-9.8)(1.5)2
= 190.2 - 11.04

That gives you the vertical displacement from the launching point. However that's not the "y" value they ask for. Read the question again. Where is the origin?

For part b...

I haven't checked x but the y co-ordinate isn't going to be -15.

hm...so is the y will have plus 15? and as for b i thought if the displacement was in regards to the place fired from and the ground 15m below is the origin wouldn't the displacement be -15? and I still don't really get how to get the answer to them especially factoring in ark and gravity

golbez22 said:
hm...so is the y will have plus 15?
Yes. yi = +15.
and as for b i thought if the displacement was in regards to the place fired from and the ground 15m below is the origin wouldn't the displacement be -15?
Yes, the vertical displacement is -15m, but I think it's clear that b is asking for the horizontal displacement.

I haven't checked x but the y co-ordinate isn't going to be -15.

Oops sorry I misread part (b) of the question. It says "displacement when the arrow lands in regards to where it was shot from" so yes the y co-ordinate will be -15.

Okay time for an update:
A.) 120.5m(105.50 + 15m height),178m
B.)_m,-15m
C.)
I have deduced to answer the last two I need how long the flight was...and I do not know how to do that.

golbez22 said:
Okay time for an update:
A.) 120.5m(105.50 + 15m height),178m
B.)_m,-15m
C.)
I have deduced to answer the last two I need how long the flight was...and I do not know how to do that.
Golbez22, it would be much easier to help you if you were to post all your working.
You have the equation yf = yi + vi t + 1/2 a t2 for the vertical. You know yi, vi, yf and a. Solve the quadratic.

golbez22 said:
Okay time for an update:
A.) 120.5m(105.50 + 15m height),178m

Nope. Which is the horizontal and which is the vertical co-ordinate? Which one do you need to add 15m to ?

## 1. What is final velocity?

Final velocity is the speed and direction of an object at a specific point in time, after undergoing a change in velocity.

## 2. How is final velocity calculated?

Final velocity can be calculated using the following formula: vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.

## 3. What is displacement?

Displacement is the overall change in position of an object, taking into account both the distance and direction traveled.

## 4. How is displacement calculated?

Displacement can be calculated by subtracting the initial position from the final position of an object. It can also be calculated using the formula: d = vit + 1/2at^2, where d is displacement, vi is initial velocity, t is time, and a is acceleration.

## 5. What are some real-world applications of finding final velocity and displacement?

Finding final velocity and displacement is important in many fields, including physics, engineering, and sports. It can be used to analyze the motion of objects, such as cars on a racetrack or projectiles in flight. It is also used in designing structures and machines to ensure their safety and efficiency.