How can I use the range equation to find the initial velocity of a projectile?

In summary, the football was kicked with a velocity of approximately 22.9 m/s. To solve for this, the equation Dy(t) = -.5at^2 + Vit + y0 was used, with the known values of hang time (4.6 s) and distance (23m). The x and y components were then found using the equations Dx=Vx(t) and Dy(t) = -.5at^2 + Vit + y0, and the final velocity was calculated using the Pythagorean theorem. The equation was also tested using the range equation and proved to be accurate.
  • #1
Havenater23
38
0
1. A football is kicked so that is had a hang time for 4.6 s and hits the ground 23m down the field ?
What was the velocity of the football when it was kicked?
2. I used the Dx=Vx(t), don't know what to use after that.
3. Can someone show step by step how to get this, I'm having trouble trying to get an answer.
Can anyone just show me the equation I would use after that. I know I can find the xi and xf , but how do I find the yi or yf?
 
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  • #2
Think about this problem in terms of components:

hang time is vertical, distance is horizontal. you should also used the equation Dy(t) = -.5at^2 + Vit + y0. from there, you can get the y component, then just find sqrt(Vx^2 + Vy^2)
 
  • #3
Well this is how I set it up, similar to yours : dy= vi(t) + 0.5(a)(t)^2

I did that have got this: dy= vi(4.6) + 103.684
I didn't take into consideration that 9.8 is negative so sorry
But where do I go from there, I don't know how to solve the rest
 
  • #4
You know the x distance: x0 = 0, xf = 23m, so 23 = Vx * t gives you Vx
you have the y time: solve for Vy with 0 = Dy(t). there will be 2 answers: 0 and the Vy you are looking for
 
  • #5
Yeah, I know about competent breakdown. I got like 22.9 m/s for the Viy.I tested it using the range equation and it worked well. Thank you so much , it really did help me !
 

FAQ: How can I use the range equation to find the initial velocity of a projectile?

1. What is a projectile at an angle?

A projectile at an angle refers to an object that is launched into the air at an angle, rather than straight up or down. This angle is known as the launch angle and can greatly affect the path and distance the projectile travels.

2. How does the launch angle affect the trajectory of a projectile?

The launch angle of a projectile has a significant impact on its trajectory. A higher launch angle will result in a longer flight time and a longer horizontal distance traveled. A lower launch angle will result in a shorter flight time and a shorter horizontal distance traveled.

3. What is the relationship between the launch angle and the initial velocity of a projectile?

The launch angle and initial velocity of a projectile are directly related. The initial velocity is the speed at which the object is launched, and the launch angle determines the direction of this velocity. As the launch angle increases, the initial velocity will be divided into vertical and horizontal components, with the horizontal component decreasing and the vertical component increasing.

4. How does air resistance affect the motion of a projectile at an angle?

Air resistance, also known as drag, can significantly affect the motion of a projectile at an angle. As the projectile travels through the air, it experiences a force in the opposite direction of its motion due to air resistance. This force can cause the projectile to slow down and decrease its horizontal and vertical distances traveled.

5. Can a projectile at an angle follow a parabolic path?

Yes, a projectile at an angle follows a parabolic path, assuming there is no air resistance. This means that the projectile's vertical displacement will follow a quadratic equation, while its horizontal displacement will follow a linear equation. However, with the presence of air resistance, the path may deviate from a perfect parabola.

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