# Projectile Motion: An Arrow Shot & Landed at Different Points

• Marvels
In summary, the problem involves an arrow being shot at an initial velocity of 45 m/s and 52 degrees above the horizontal. The arrow lands on a 5 m high roof of a house, having been shot from a height of 1.5 m. The questions being asked are whether the arrow can pass over a 50 m high tree located 75 m away, what its total time of flight is, and how far away is the house. The relevant equations for solving this problem are provided, including d = vit + 1/2at^2, v = d/t, and a = vf-vi/t. The maximum height of the arrow is calculated to be 65.43 m, and the time of
Marvels

## Homework Statement

An Arrow is shot from an initial velocity of 45 m/s 52 degrees above the horizontal. It lands on a 5 m high roof of a house. The arrow is shot from a height of 1.5 m.

(v) Would it be able to pass over a 50 m high tree located 75 m away?
(vi) What is its' total time of flight?
(vii) How far away is the house?

d = vit +1/2at^2
v=d/t
a = vf-vi/t

## The Attempt at a Solution

I've calculated the max height of the arrow; 65.43 m, and the time, 3.6 s.

I don't know how to calculate the horizontal displacement of an object starting 1.5 m off the ground.

Marvels said:

## Homework Statement

An Arrow is shot from an initial velocity of 45 m/s 52 degrees above the horizontal. It lands on a 5 m high roof of a house. The arrow is shot from a height of 1.5 m.

(v) Would it be able to pass over a 50 m high tree located 75 m away?
(vi) What is its' total time of flight?
(vii) How far away is the house?

d = vit +1/2at^2
v=d/t
a = vf-vi/t

## The Attempt at a Solution

I've calculated the max height of the arrow; 65.43 m, and the time, 3.6 s.

I don't know how to calculate the horizontal displacement of an object starting 1.5 m off the ground.

How does the starting height affect the horizontal displacement? What would happen to the arrow if you moved the ground up 1.5 m?

SteamKing said:
How does the starting height affect the horizontal displacement? What would happen to the arrow if you moved the ground up 1.5 m?

Do I add 1.5 m to the regular displacement? (Do I do the same with y disp, too?)

Marvels said:
Do I add 1.5 m to the regular displacement?
No, why do you think that might be valid? Please don't make wild guesses.
What you can do is make shift of origin, provided you do it consistently. I.e. add or subtract a number from all horizontal coordinates, and likewise (but maybe a different number) from all heights.

## 1. What is projectile motion?

Projectile motion is the motion of an object that is launched into the air and moves along a curved path due to the force of gravity.

## 2. How is projectile motion affected by the angle of launch?

The angle of launch affects the range and height of the projectile. A higher angle will result in a longer range and higher height, while a lower angle will result in a shorter range and lower height.

## 3. How does air resistance affect projectile motion?

Air resistance can affect the trajectory and speed of a projectile. It can cause the projectile to slow down and deviate from its intended path.

## 4. What factors can affect the landing point of a projectile?

The landing point of a projectile can be affected by the angle of launch, initial velocity, air resistance, and the presence of external forces such as wind.

## 5. How is the range of a projectile calculated?

The range of a projectile can be calculated using the formula range = (velocity^2 * sin(2*angle))/g, where velocity is the initial velocity, angle is the angle of launch, and g is the acceleration due to gravity.

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