Finding initial velocity in free fall with given meters.

[Crusaderking1]

Homework Statement

A juggler throws a ball just so it reaches the ceiling at 3.0 meters. (3m above hand)
How do I solve for initial velocity?

Homework Equations

The Attempt at a Solution

 

[PeterO]

Homework Statement

A juggler throws a ball just so it reaches the ceiling at 3.0 meters. (3m above hand)
How do I solve for initial velocity?

Homework Equations

The Attempt at a Solution

You would use the fact that falling from the ceiling to his hand mirrors his toss to the ceiling.
One is travel up - the other down
One starts at high speed and finished at zero speed, the other starts at zero speed and finishes at the same high speed.

 

[Quantum Mind]

Recall the equations for motion, time and displacement and see which one fits. For that you have to see what values you know and what you do not know.

 

[Crusaderking1]

thanks.

 

[rwisz]

To solve for the initial velocity, we can use the formula for free fall motion:

h = (1/2)gt^2 + v0t + h0

Where:
h = height (in this case, 3 meters)
g = acceleration due to gravity (9.8 m/s^2)
t = time (unknown)
v0 = initial velocity (unknown)
h0 = initial height (in this case, 0 meters)

We can rearrange this formula to solve for v0:

v0 = (h - (1/2)gt^2)/t

Since we know h = 3 meters, g = 9.8 m/s^2, and h0 = 0 meters, we can substitute these values into the formula:

v0 = (3 - (1/2)(9.8)t^2)/t

To solve for t, we can use the quadratic formula:

t = (-b ± √(b^2 - 4ac))/2a

Where:
a = -4.9 (since the coefficient of t^2 is -4.9 in the above equation)
b = 0 (since the coefficient of t is 0 in the above equation)
c = -9 (since 3 - (1/2)(9.8)t^2 = 0 when the ball reaches the ceiling)

Plugging in these values, we get:

t = (-0 ± √(0^2 - 4(-4.9)(-9)))/2(-4.9)

Simplifying, we get:

t = (-0 ± √176.4)/(-9.8)

Therefore, the possible values for t are:

t = 0.844 seconds or t = -2.094 seconds

Since time cannot be negative, we can discard the negative value and conclude that the time it takes for the ball to reach the ceiling is approximately 0.844 seconds.

To solve for v0, we can substitute this value into the formula we derived earlier:

v0 = (3 - (1/2)(9.8)(0.844)^2)/0.844

Simplifying, we get:

v0 = 4.14 m/s

Therefore, the initial velocity of the ball when it is thrown is approximately 4.14 m/s.