Projectile motion - where will the ball land

In summary, a ball is thrown from the top of a 40m building at a 20m/s velocity, aiming for a friend 30m away. Using Pythagoras theorem, the total distance traveled by the ball is 50m. With the angle of 53°, the horizontal velocity is 16m/s and the vertical velocity is 12m/s. To find the time it takes for the ball to reach the ground, the formula s = ut + 1/2 at2 can be used, with an initial vertical velocity of 0. The direction of positive and negative vectors can be chosen, but must be consistent throughout the problem.
  • #1
physics kiddy
135
1

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.

Homework Equations





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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  • #2
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.
 
  • #3
physics kiddy said:

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.

Homework Equations





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.
 

1. What is projectile motion?

Projectile motion is the motion of an object through the air or space under the influence of gravity. It follows a curved path called a parabola.

2. What factors affect the landing point of a projectile?

The factors that affect the landing point of a projectile include the initial velocity, angle of launch, air resistance, and the force of gravity.

3. How is the landing point of a projectile calculated?

The landing point of a projectile can be calculated using the equations of motion, taking into account the initial velocity, angle of launch, and the force of gravity. These calculations can also be done using computer simulations.

4. How does air resistance affect the trajectory of a projectile?

Air resistance can affect the trajectory of a projectile by slowing it down and altering its path. This is why objects with greater surface area, like a feather, will experience more air resistance and have a different trajectory compared to an object with less surface area, like a bullet.

5. Can the landing point of a projectile be predicted with 100% accuracy?

No, the landing point of a projectile cannot be predicted with 100% accuracy due to external factors such as air resistance and human error. However, with precise measurements and calculations, it is possible to make accurate predictions and minimize errors.

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