Calculating Projectile Motion: Solving for Distance and Height

In summary, the problem involves a ball being thrown from a window with an initial velocity of 8.20 m/s at an angle of 15.0° below the horizontal. The ball strikes the ground after 3.00 seconds and the task is to find the horizontal distance and height from which the ball was thrown. The equations used are r= v^2(sin2theta)/g and h= v^2(sintheta)2/2g. To solve the problem, the velocity vector is resolved into horizontal and vertical components and the equations are applied.
  • #1
physics_geek
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Homework Statement


A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 8.20 m/s at an angle of 15.0° below the horizontal. It strikes the ground 3.00 s later.
(a) How far horizontally from the base of the building does the ball strike the ground?
4.90wrong check mark m
(b) Find the height from which the ball was thrown.
wrong check mark m
(c) How long does it take the ball to reach a point 10.0 m below the level of launching?



Homework Equations


i think the equations are r= v^2(sin2theta)/g
h= v^2(sintheta)2/2g


The Attempt at a Solution


i tried pluggin in the values to get how far it traveled and the height..but I am getting it wrong

any help would be appreciated
 
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  • #2
Work out the velocity component downward.
Then it's just the normal moving object equations except the initial velocity isn't zero.
 
  • #3
im not sure wat you mean by that

make the velocity -8.2?
im so confused
 
  • #4
You need to resolve the velocity vector into horizontal and vertical components. Then, what mgb is saying, is you consider the vertical component.
 
  • #5
o ok into two different components

so they give me 8.2 m/s
thats my resultant vector rite?

so i just do 8.2(cos15) ??
 
  • #6
Draw a diagram (triangle) - it should be obvious how much of the diagonal speed goes horizontally and how much vertically.
 
  • #7
alrite cool
thanks a lot guys
 

1. What is the definition of free fall?

Free fall is the motion of an object under the influence of gravity alone. This means that there are no other forces acting on the object, such as air resistance or friction.

2. What is the acceleration of an object in free fall?

The acceleration of an object in free fall is the same as the acceleration due to gravity, which is approximately 9.8 meters per second squared (9.8 m/s²). This means that for every second an object is in free fall, its velocity will increase by 9.8 m/s.

3. How can you calculate the distance an object in free fall has fallen?

The distance an object falls in free fall can be calculated using the equation d = ½ * g * t², where d is the distance, g is the acceleration due to gravity, and t is the time in seconds.

4. Does the mass of an object affect its rate of free fall?

No, the mass of an object does not affect its rate of free fall. All objects, regardless of their mass, will accelerate at the same rate due to gravity.

5. What is the difference between free fall and terminal velocity?

Free fall is the motion of an object under the influence of gravity alone, while terminal velocity is the maximum velocity an object can reach when falling through a fluid, such as air. In free fall, there is no opposing force to slow down the object's acceleration, while in terminal velocity, the object's acceleration is balanced by the opposing force of air resistance.

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