# Projectile motion - where will the ball land

## Homework Statement

A boy standing on the top of a building 40m high throws a ball directly aiming to his friend standing on the ground 30m away from the base of the building. If the projection velocity is 20m/s. Find how short will the ball fall from his friend.

## The Attempt at a Solution

From the picture I have attached, AB = 40 m
BC = 30 m
Using pythagoras theorem, we have AC = 50 m

Using tan θ = p/b we have tan θ = 40/30 so, θ = tan-1(4/3) = 53°

Now, breaking the components,
Horizontally:
20 * cos53° = 16 m/s

Vertically,
20 * sin 53° = 12m/s

My problem begins here :

1) Which formula do I use, s = ut + 1/2 at2 or v = u + at to find the time it takes to reach ground vertically.

2) What's the sign of u and g here.

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Use the first equation, s = ut + 1/2 at2 to find the time it takes to reach the ground, u would be 0 since there is no initial vertical velocity.

## Homework Statement

A boy standing on the top of a building 40m high throws a ball directly aiming to his friend standing on the ground 30m away from the base of the building. If the projection velocity is 20m/s. Find how short will the ball fall from his friend.

## The Attempt at a Solution

From the picture I have attached, AB = 40 m
BC = 30 m
Using pythagoras theorem, we have AC = 50 m

Using tan θ = p/b we have tan θ = 40/30 so, θ = tan-1(4/3) = 53°

Now, breaking the components,
Horizontally:
20 * cos53° = 16 m/s

Vertically,
20 * sin 53° = 12m/s

My problem begins here :

1) Which formula do I use, s = ut + 1/2 at2 or v = u + at to find the time it takes to reach ground vertically.

2) What's the sign of u and g here.
1) You have only intial velocity and you can choose which is appropriate.
2) You can take going up as positive or down as positive. Once you make a convention on the sign of direction, all vectors direction should follow this convention.