# Projectile motion with people moving

• sunbunny
In summary, the conversation discusses solving a problem involving a quarterback throwing a football to a tight end for a game-winning touchdown. The technique involves manipulating two equations and setting them equal to each other, resulting in a quadratic equation. By solving for t using the quadratic formula and plugging it into a specific equation, the answer for the speed of the throw can be obtained.
sunbunny
I'm having trouble with this problem as well:

Quarterback Fred is going to throw a pass to tight end Doug. Doug is 20 m in front of Fred and running straight away at 6.0 m/s when Fred throws the 500 g football at a 40 angle. Doug catches the ball without having to alter his speed and runs for the game-winning touchdown.

How fast did Fred throw the ball?

I don't even know where to start with so so if anyone can help me get started that would be great.

Thanks

Look at these two equations and figure out how and why they work:

$$6t+20=v_{0}\cos(\theta)t$$

$$v_{0}\sin(\theta)t=\frac{gt^{2}}{2}$$

Solve each in terms of $v_{0}$, equate one equation to the other, solve for t, and then plug it into a formula to find $v_{0}$.

Okay, so when i solved for vo i for:

vo= 6t+20/cost and vo= gt^2/2sint

then i made these equations equal to each other:

6t + 20/cost = gt^2/sint

but when i solve for t, the value that i get donesn't work. if you could explain how to solve for t properly that would be geat.

sunbunny said:
Okay, so when i solved for vo i for:

vo= 6t+20/cost and vo= gt^2/2sint

then i made these equations equal to each other:6t + 20/cost = gt^2/sint

but when i solve for t, the value that i get donesn't work. if you could explain how to solve for t properly that would be geat.

The equation you end up with is a quadratic. Manipulate it to form $$ax^{2}+bx+c=0$$, and solve for x. You will get two roots$-$only one will be applicable.

Last edited:
okay this time when i did that i got:

12sint^2 + 40sint=gcost^3

-gcost^3+ 12sint^2 + 40sint=0

t(-gcost^2 + 12sint =40sin)=0

i solved for inside the brackets using the quadratic formula and i got 2.43 for my time and then i put it back into one of the equations and i got 78m/s however i still got the wrong answer.

I was wondering if you could please check over my work to make sure that I'm not missing anything. Thanks!

sunbunny said:
okay this time when i did that i got:

12sint^2 + 40sint=gcost^3

-gcost^3+ 12sint^2 + 40sint=0

t(-gcost^2 + 12sint =40sin)=0

i solved for inside the brackets using the quadratic formula and i got 2.43 for my time and then i put it back into one of the equations and i got 78m/s however i still got the wrong answer.

I was wondering if you could please check over my work to make sure that I'm not missing anything. Thanks!

2.43 s is the correct time. Which equation did you plug it back into?

i put it into the 6t+20/cost equation

sunbunny said:
i put it into the 6t+20/cost equation

Put it into:

$$y=v_{0}\sin(\theta)t-\frac{gt^{2}}{2}$$

Remember, at the time you've specified, y will have a certain value.

Your question is solved with this equation.

okay i got it now, thank you for your help!

## 1. How does a person's motion affect the trajectory of a projectile?

The motion of a person can impact the trajectory of a projectile in several ways. First, if the person is the one launching the projectile, their initial velocity and angle of release can significantly influence the path it takes. Additionally, if the person is moving while the projectile is in the air, their motion can alter the position of the projectile at any given time, resulting in a different final landing spot.

## 2. Can a person's movement impact the range of a projectile?

Yes, a person's movement can definitely affect the range of a projectile. By changing the angle or speed at which they launch the projectile, they can alter the overall distance it travels. Additionally, if the person moves while the projectile is in the air, their motion can cause the projectile to land further or closer to the target.

## 3. How does the weight of a person impact projectile motion?

The weight of a person can affect projectile motion in a few ways. If the person is the one launching the projectile, their weight can influence the initial velocity and angle of release. However, once the projectile is in the air, the person's weight does not directly impact its path. However, if the person is on a moving platform or vehicle, their weight can affect the overall motion and trajectory of the projectile.

## 4. How does air resistance affect projectile motion with people moving?

Air resistance can have a significant impact on projectile motion, especially when people are moving. The speed and direction of the person's motion can increase or decrease the amount of air resistance the projectile experiences. This can alter the projectile's velocity, trajectory, and ultimately, its landing spot.

## 5. Is it possible to accurately predict the motion of a projectile with people moving?

While it is possible to make predictions about the motion of a projectile with people moving, it may not always be accurate. The complexity of multiple moving objects and varying factors such as initial velocity, angle of release, and air resistance can make it challenging to make precise predictions. However, with careful measurements and calculations, it is possible to make relatively accurate predictions about projectile motion with people moving.

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