Using quadratic formula to find time [projectile motion]

In summary, the student is trying to find time in a projectile equation using the Y components, but gets an error when trying to solve for t.
  • #1
camcognito
2
0
1. Homework Statement
I'm doing lab, and to start we have to find ΔX of a projectile launched an angle. The first step for us is to find time, and to make it easier our teacher recommended us to first set the angle to zero, and find time like that.

I don't have enough X information to find time yet, so I have to use the Y components I think

X
ΔX= .153 M
Φ = 0°
Y
AY = 9.8m/s2
ΔY = -.96 M.
Φ = 0°
Viy = 0 ?

Homework Equations


I'm supposed to take the equation ΔY = Viyt + 1/2ayt2 and make it into quadratic formula. For some reason t = √2ΔY/AY won't work and we're supposed to use quadratic formula

The Attempt at a Solution


[/B]
Since I'm launching the projectile from 0°, I thought the Viy would equal 0. However, when I try to plug that into the quadratic formula, there's a 0 for one of the variables and it doesn't work.

I'm getting -4.9t2 + 0 + .96 = 0; I think I'm doing something wrong in the middle but I'm not sure what to fix.
 
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  • #2
camcognito said:
1. Homework Statement
I'm doing lab, and to start we have to find ΔX of a projectile launched an angle. The first step for us is to find time, and to make it easier our teacher recommended us to first set the angle to zero, and find time like that.

I don't have enough X information to find time yet, so I have to use the Y components I think

X
ΔX= .153 M
Φ = 0°
Y
AY = 9.8m/s2
ΔY = -.96 M.
Φ = 0°
Viy = 0 ?

Homework Equations


I'm supposed to take the equation ΔY = Viyt + 1/2ayt2 and make it into quadratic formula. For some reason t = √2ΔY/AY won't work and we're supposed to use quadratic formula

The Attempt at a Solution


[/B]
Since I'm launching the projectile from 0°, I thought the Viy would equal 0. However, when I try to plug that into the quadratic formula, there's a 0 for one of the variables and it doesn't work.

I'm getting -4.9t2 + 0 + .96 = 0; I think I'm doing something wrong in the middle but I'm not sure what to fix.

The equation -4.9t2 + 0 + .96 = 0 is correct, just solve it for t.
 
  • #3
ehild said:
The equation -4.9t2 + 0 + .96 = 0 is correct, just solve it for t.
Wow... it was that simple. Thanks, I've been overthinking a lot of equations recently
 

1. How does the quadratic formula help in finding the time in projectile motion?

The quadratic formula is a mathematical formula that helps solve quadratic equations. In the context of projectile motion, the height of an object can be represented by a quadratic equation, where time is the variable. By using the quadratic formula, we can solve for the time at which the object reaches a certain height or distance.

2. What are the variables in the quadratic equation for projectile motion?

The variables in a quadratic equation for projectile motion are the initial velocity (u), the acceleration due to gravity (g), and the initial height (h). These variables are used to represent the motion of the object in the equation h = ut + 1/2 gt^2, where h is the height at time t.

3. Can the quadratic formula be used for all types of projectile motion?

Yes, the quadratic formula can be used for all types of projectile motion, as long as the motion can be represented by a quadratic equation. This includes both horizontal and vertical projectile motion.

4. How accurate is the time calculated using the quadratic formula?

The time calculated using the quadratic formula is accurate as long as the initial conditions (velocity, angle, and height) are known and the motion is not affected by external factors such as air resistance. However, in real-life scenarios, there may be slight variations due to factors such as air resistance and human error in measuring the initial conditions.

5. Are there any limitations to using the quadratic formula for projectile motion?

The quadratic formula assumes that the acceleration due to gravity is constant and the motion is not affected by external factors. In reality, these assumptions may not always hold true, leading to slight inaccuracies in the calculated time. Additionally, the quadratic formula may not be applicable for complex projectile motion scenarios, such as those involving multiple objects or non-uniform gravitational fields.

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