Horizontal range of a projectile

In summary, a ball is thrown from a window with an initial velocity of 7.80 m/s at an angle of 15.0° below the horizontal. After 6.00 seconds, it reaches the ground. To determine the horizontal distance traveled, the equation Vx = xsinTheta is used, resulting in an answer of 12.11m. However, the correct answer is 45.2m, indicating that Vx = xcosTheta should have been used instead.
  • #1
dink87522
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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 7.80 m/s at an angle of 15.0° below the horizontal. It strikes the ground 6.00 s later.
(a) How far horizontally from the base of the building does the ball strike the ground?


Homework Equations



Vx = xsinTheta

DeltaX = Vx . t

The Attempt at a Solution



Vx = 7.8sin(15) = 2.02 m/s^-1

DeltaX = (2.02)(6) = 12.11m

Something is seriously wrong in my answer although I can't see what. The answer should be 45.2m.
 
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  • #2
I realize I am using Vx = xsinTheta instead of Vx = xcosTheta, although why is it that? When drawing a triangle of this and doing the trig, I get the first equation, could someone please explain this.
 

1. What is the horizontal range of a projectile?

The horizontal range of a projectile is the maximum distance it travels horizontally from its initial position to its final position.

2. How is the horizontal range of a projectile calculated?

The horizontal range of a projectile can be calculated using the formula R = v0 * cosθ * t, where R is the horizontal range, v0 is the initial velocity, θ is the angle of launch, and t is the time of flight.

3. Does air resistance affect the horizontal range of a projectile?

Yes, air resistance can affect the horizontal range of a projectile. If the projectile is launched at a high speed or at a steep angle, air resistance can decrease its horizontal range by slowing it down.

4. Can the horizontal range of a projectile be greater than its vertical displacement?

Yes, the horizontal range of a projectile can be greater than its vertical displacement. This is because the horizontal and vertical components of a projectile's motion are independent of each other.

5. How does the horizontal range of a projectile change with increasing launch angle?

The horizontal range of a projectile increases with increasing launch angle, reaching a maximum at a 45-degree angle. After this point, the range decreases as the angle increases further. This is due to the fact that the vertical component of the projectile's motion increases, while the horizontal component remains constant.

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