Express Max height in terms of g and T? ?

In summary, the conversation discusses how to express maximum height in terms of gravity (g) and time (T). The formula V_0y*T + 1/2gT^2 is mentioned as being correct, but it is important to find the time when the object reaches its maximum height and its velocity is 0. The discussion also mentions the importance of considering the signs of the initial velocity (V_0) and gravity (g) in determining maximum height.
  • #1
scke0803
2
0
Express Max height in terms of g and T?!?

I need to express the y_max in terms of g and T...

do i need to put in my V_0y value? or leave it as a variable?









i've tried V_0y*T + 1/2gT^2
 
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  • #2


Vo is not a variable, it is constant. Your formula is correct for the height at time T. You have to find the time when the body reaches it maximum height and does not rise any more. What is its velocity at that instant?

ehild
 
  • #3


Velocity at maximum height is 4.229 m/s
 
  • #4


So it moves further upward. Why is it maximum height then?
Try to throw up something and watch the velocity.

And mind the signs. There is a maximum height if Vo points upward (and g downward) . Vo and g have to be of opposite signs. ehild
 
Last edited:
  • #5
, but i'm not sure if that's correct.

Yes, your expression of y_max = V_0y*T + 1/2gT^2 is correct. This is the equation for maximum height in terms of initial velocity (V_0y), time (T), and gravitational acceleration (g). The initial velocity, V_0y, can be either a known value or left as a variable depending on the specific problem.
 

1. How do you express maximum height in terms of acceleration due to gravity (g) and time (T)?

The maximum height (h) of an object thrown vertically upwards can be expressed as h = (1/2)gT2, where g is the acceleration due to gravity and T is the time taken.

2. What is the relationship between maximum height and acceleration due to gravity?

The maximum height achieved by an object depends on the acceleration due to gravity. A higher value of g will result in a greater maximum height, while a lower value of g will result in a lower maximum height.

3. Can you calculate the maximum height of an object without knowing the time taken?

Yes, if the initial velocity (u) and final velocity (v) of the object are known, the maximum height can be calculated using the formula h = (v2 - u2)/(2g). This formula is derived from the equation v = u + gt, where v is the final velocity, u is the initial velocity, and t is the time taken.

4. How does the initial velocity of an object affect its maximum height?

The initial velocity (u) of an object affects its maximum height in the same way as acceleration due to gravity. A higher initial velocity will result in a greater maximum height, while a lower initial velocity will result in a lower maximum height.

5. Is the maximum height of an object always positive?

Yes, the maximum height of an object is always positive because it is a measure of the vertical distance from the ground. In some cases, it may be considered negative if the reference point is taken as the highest point reached by the object, but in general, it is always considered positive.

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