Vectors and Trigonometry Homework Help

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SUMMARY

The discussion focuses on solving a physics problem involving projectile motion, specifically a stone thrown straight up with an initial speed of 15.0 m/s. The participant initially calculated the time to reach an altitude of 8.0 m as 1.43 seconds, while the correct answers are 0.68 seconds and 2.4 seconds. The final velocity (Vf) at that height is confirmed to be 8.3 m/s. The relevant equation used is D = v0t + (1/2)at², and the discussion highlights the importance of solving quadratic equations to find multiple time solutions.

PREREQUISITES
  • Understanding of basic physics concepts, particularly projectile motion.
  • Familiarity with the kinematic equations, specifically D = v0t + (1/2)at².
  • Knowledge of quadratic equations and their solutions.
  • Ability to perform calculations involving initial velocity, acceleration, and displacement.
NEXT STEPS
  • Study the derivation and application of the kinematic equations in projectile motion.
  • Learn how to solve quadratic equations, including the quadratic formula.
  • Explore the concept of multiple solutions in projectile motion scenarios.
  • Practice solving similar physics problems involving vertical motion and time calculations.
USEFUL FOR

Students studying physics, educators teaching kinematics, and anyone seeking to improve their problem-solving skills in projectile motion scenarios.

Lui4
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Homework Statement
A stone is thrown straight up with a speed of 15.0m/s
(a) How fast will it be moving when its altitude is 8.0m above the point from which it was thrown? How much time elapses while the stone is reaching that height?
(b) Is there one answer or are there two answers? Why?
Relevant Equations
D=vot+(1/2) (a) (t)^2
Hey, I am new to this community and I am in need of help with this physics problem. I have used the formula above and the answer I get is 1.43s. The correct two answers are 0.68s and 2.4s. For the Vf the answer is 8.3 m/s.
 
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Lui4 said:
Homework Statement:: A stone is thrown straight up with a speed of 15.0m/s
(a) How fast will it be moving when its altitude is 8.0m above the point from which it was thrown? How much time elapses while the stone is reaching that height?
(b) Is there one answer or are there two answers? Why?
Relevant Equations:: D=volt+(1/2) (a) (t)^2

Hey, I am new to this community and I am in need of help with this physics problem. I have used the formula above and the answer I get is 1.43s. The correct two answers are 0.68s and 2.4s. For the Vf the answer is 8.3 m/s.
If you would like someone to point out where you went wrong it would be helpful if you were to post your working.
 
Hey, thanks for the quick reply. Hope this helps understand the problem better!

1607937531507.png

1607937606153.png


1607937567714.png
 
You don't seem to know how to solve quadratic equations.
 
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Oh, okay.
 
A guide on how to solve a quadratic equation Quadratic equation - Wikipedia

If you are bored to read all that (lol) here is the core of that article:
A quadratic equation ##ax^2+bx+c=0## has (in the most general case) two roots:
$$x_1=\frac{-b+\sqrt{b^2-4ac}}{2a}$$ and $$x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}$$
 
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Thank you for your help, I’ll keep this in mind when looking at the question!
 
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