a juggler throws a ball into the air, releasing it 5 feet above ground with an initial velocity if 15 fps. she catches the ball in thr other hand 5 feet above the ground. How long was the ball in the air?
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Final answer:
The juggled ball was in the air for roughly 0.94 seconds. Using the principles of projectile motion and gravity, you calculate the time for the ball to rise to its peak and then double this value to get the total time the ball is in the air as it follows the same path back down.
Explanation:
The question is about determining the time a juggled ball stays in the air when thrown up at a particular speed and height. The principles of projectile motion and gravity apply here. The time taken for the ball to rise and fall back to the same height can be found using the physics concept of free fall. While the ball is in the air, it rises and then falls to a final position which is equal to its starting altitude. This is because the ball is thrown and caught at the same height.
From the facts we have, the initial vertical speed is 15 fps (feet per second). Since the acceleration due to gravity is -9.8 m/s² or approximately -32.2 fps² (note that it is negative as it is acting downward), we can use the following equation of motion which is derived from Newton's second law:
final velocity = initial velocity + (acceleration x time)
In this case, the final velocity when the ball reaches the peak of its flight is 0 (since it stops for a moment before falling again), and the acceleration is -32.2 fps². If we rearrange the equation to solve for time (t), we get:
t = (Final velocity - Initial velocity) / acceleration. Substituting the values we get:
t = (0 - 15) / -32.2 = 0.47 s
This is the time taken for the ball to go up. However, the ball takes the same amount of time to come down, so we multiply this by 2 to get the total time the ball is in the air:
Total time = 0.47 x 2 = 0.94 seconds, approximately.
So, the ball was in the air for roughly 0.94 seconds.
Learn more about Projectile Motion here:
#SPJ2
Here, you don't need to calculate velocity, but rather time. Start with this equation:
v = v0 + a t^2, where v is the velocity at time t, v0 is the initial velocity, a is the acceleration due to gravity (denoted by g instead of a), and t is the elapsed time.
You are told that v0 is 15 ft/sec. Set v = to 0, as the ball stops moving for the tiniest instant at the top of its trajectory. Use g = - 32 ft (per second squared).
Then 0 = 15 ft/sec - 32 [ft/(seconds squared)] t.
Solve this for t. This is the time required for the ball to come to a complete stop at the top of its trajectory.
Finally, multiply this time by 2, since the ball begins to fall and returns to its original height.
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Answer:
75%
Step-by-step explanation:
We know that the quarterback has completed 30 of 40 passes. This means that the ratio of completed passes to total passes is 30:40. Converting this to a fraction, we get 30/40, which can be simplified to 3/4. 3/4 as a percentage is 75%. Therefore, the final answer is 75%.
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25 + (12 * 10 + -1x * 10) = 5(2x + -7)
25 + (120 + -10x) = 5(2x + -7)
Combine like terms: 25 + 120 = 145145 + -10x = 5(2x + -7)
Reorder the terms:
145 + -10x = 5(-7 + 2x)
145 + -10x = (-7 * 5 + 2x * 5)
145 + -10x = (-35 + 10x)
Solving145 + -10x = -35 + 10x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-10x' to each side of the equation.
145 + -10x + -10x = -35 + 10x + -10x
Combine like terms: -10x + -10x = -20x145 + -20x = -35 + 10x + -10x
Combine like terms: 10x + -10x = 0145 + -20x = -35 + 0145 + -20x = -35
Add '-145' to each side of the equation.145 + -145 + -20x = -35 + -145
Combine like terms: 145 + -145 = 00 + -20x = -35 + -145-20x = -35 + -145
Combine like terms: -35 + -145 = -180-20x = -180
Divide each side by '-20'.
x = 9
Simplifyingx = 9.
Hope this helps you ! =')
b. How much does she receive on average for a page?
if able answer both also its Rate (unit rate's possilbe)
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10: 2 5
GCF: 2
The greatest common factor is 2
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250 miles / 50 miles per hour = 5 hours
It will take 5 hours to travel 250 miles.
250 divided by 50 = 5