Introductory physics: Time for a ball thrown vertically to reach maximum height

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SUMMARY

The discussion centers on calculating the time for a ball thrown vertically to reach maximum height using the freefall equation. A participant verified their answer using the equation distance = 1/2 (g)(t^2) and calculated the maximum height (d) as 11.4 meters with the formula Vf^2 = Vi^2 + (2)(a)(d). However, the primary focus should be on determining the time in seconds to reach that height, rather than the height itself. Clarifications were made regarding the interchangeability of variables "x" and "d".

PREREQUISITES
  • Understanding of kinematic equations in physics
  • Familiarity with freefall motion and gravitational acceleration (g = -9.8 m/s²)
  • Knowledge of initial and final velocity concepts
  • Ability to manipulate algebraic equations for problem-solving
NEXT STEPS
  • Learn how to derive time from kinematic equations in vertical motion
  • Study the implications of gravitational acceleration on projectile motion
  • Explore the use of different kinematic equations for various motion scenarios
  • Practice solving problems involving maximum height and time in freefall contexts
USEFUL FOR

Students studying introductory physics, educators teaching kinematics, and anyone interested in understanding projectile motion and freefall calculations.

danielsmith123123
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Homework Statement
A 3 kg ball is thrown vertically into the air with an initial velocity of 15 m/s. What is the time it takes for the ball to reach its maximum height?
Relevant Equations
Vf =vi +at
Vf^2 = Vi^2 +2ax
x = Vf t - (1/2)(a)(t^2)
x = Vi t + (1/2)(a)(t^2)
Is the answer key wrong? I keep getting the same answer and it is verified with the freefall equation distance=1/2 (g)(t^2)
IMG_5721[1120].PNG
 
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You should write the full text of the problem, not an abstract of it. Where did the value of d comes from?
 
Ok thank you, i edited the forum. I guess you can't open pictures on this website, but i calculated d with Vf^2=Vi^2 +(2)(a)(d)
0^2 = 15^2 + (2)(-9.8)d
d = 11.4m
(I realize i probably shouldn't use "x" and "d" interchangibly)
 
You found the maximum height. The problem is asking you to find the time it takes to reach that maximum height. Your answer should be a number in seconds, not meters.
 
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danielsmith123123 said:
Ok thank you, i edited the forum. I guess you can't open pictures on this website, but i calculated d with Vf^2=Vi^2 +(2)(a)(d)
0^2 = 15^2 + (2)(-9.8)d
d = 11.4m
(I realize i probably shouldn't use "x" and "d" interchangibly)
You don't need the height but you got it OK. What is your problem? I cannot read the image you posted. It is not clear enough.
 

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