Solving Frisbee and Student Motion: A Homework Challenge

[dramallama]

Homework Statement

Just when a Frisbee passes over the head of a student at a speed of 4m/s and decelerating at a rate of 1.5 m/s², she starts to run accelerating at a rate of 1 m/s². [neglect vertical motion of Frisbee]

a)How long will it take the student to catch the Frisbee?

b) If instead of accelerating the student were able to run at a constant speed of 2 m/s as soon as the Frisbee passes her head how far would she have to run to catch it?

Homework Equations

x=x₀+V₀t+1/2at²

The Attempt at a Solution

So for part a, I figured if I made both x_frisbee and x_student equal to each other I could solve for t
x_frisbee=0+4t+(0.5)(-1.5)t²
x_student=0+0t+(0.5)(1)t²

0.5t²=4t+0.75t²
t=0s t=3.2s

And something similar for part b:
x_frisbee=0+4t+(0.5)(-1.5)t²
x_student=0+2t+(0.5)(0)t²

4t+(0.5)(-1.5)t²=2t
t=0s t=2.7s
x=(2m/s)(2.7s)=5.4m

I just wanted to know if I got these right. Thanks!

 

[Doc Al]

Looks perfect to me.

(Nitpick: Careful not to round off until the last step--especially if you're submitting your work to an online system. They can be picky.)

 

[jhae2.718]

Looks like you did everything correctly.

One caution: be careful with your signs; had you gone off of this equation, you would have gotten the result that the student will never reach the frisbee:

0.5t²=4t+0.75t²

What Doc Al says about rounding is good advice. The distance, if you carry figures through to the end, ends up at about 5.3333 m.

 

[dramallama]

Thank you for your help.

I'll make sure to hold the rounding off until the end and to check my signs next time.

 

[rwisz]

Your attempt at solving the problem is correct. To find the time it takes for the student to catch the Frisbee, you set the equations for the position of the Frisbee and the student equal to each other and solve for t. This gives you the correct answer of t = 3.2 seconds. For part b, you correctly used the equation for position to find the distance the student would have to run to catch the Frisbee, which is 5.4 meters. Great job!