Answer: the ball clears the bar by 2.48[m] as it passes through the goal posts.
Step-by-step explanation:
This question requires you to solve for two quantities. First you will need to determine how long it takes the ball to reach the goal based on its x-velocity. Second, you will use the time you calculated to determine the y-value (height) of the ball at that time. Putting these values together, you will know by how much the ball cleared the goal post.
Step 1: Finding how long it takes to reach the goal post.
1. Convert the speed of 17[m/s] into its x-component and y-component.
2. The x-component is given by 17*cos(59.4) = 8.654[m/s]
3. The y-component is given by 17*sin(59.4) = 14.633 [m/s] (Note that it makes sense that the y-component is larger because the ball is being kicked at an angle greater than 45 degrees from horizontal.)
4. Divide your 22[m] distance from the goal by the x-component of the ball's velocity to get the time it takes to reach the goal post. 22[m]/8.654[m/s] = 2.542[s]
Step 2: Find the y-coordinate of the ball at time = 2.542[s]
1. Use the formula y_final = 0.5*y_acceleration*t^2 + y_velocity_initial*t + y_position_initial
2. Substitute values to get y_f = 0.5*-9.8[m/s^2]*(2.542[s])^2 + 14.633[m/s]*2.542[s] + 0
3. Solve to obtain y_f = 5.534 [m]
4. Subtract the height of the bar to find the distance by which the ball clears the bar. 5.534[m] - 3.05[m] = 2.48[m]
Therefore, the ball clears the bar by 2.48[m] as it passes through the goal posts.
When you’re younger, it’s not so much about the type of investments you hold but more about just diligently saving. “Mutual funds or stocks? It just doesn’t matter much at this stage,” says certified financial planner Janet Gray. “Simply having a savings account means you’re in the game.”
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Answer:
y=2
x=-1
Step-by-step explanation:
2x-4y=-10
-2x-y=0
Add Together and get:
-5y=-10
y=2
put the 2 in for y in either equation to solve for x
2x-4(2)=-10
2x-8=-10
2x=-2
x=-1
To convert a mixed number to its lowest form, one needs to change the mixed number into an improper fraction and then reduce this improper fraction to the lowest possible fraction. To do these conversions, one needs to perform a few calculations. One also has to understand the definitions of "mixed number," "improper fraction" and "proper fraction."
A proper fraction is a fraction that has a lower number in the numerator and a higher number in denominator, such as the fraction three-fourths. An improper fraction is the inverse of this, which entails the higher number in numerator and lower number in the denominator, like 5/3. A mixed number is a whole number with a fraction, such as 1 3/4.
To convert the mixed number 1 3/4, one has to multiply the denominator 4 by the whole number 1 that gives 4, add this 4 to the 3 in the numerator to get 7 and place 7 over the denominator to find the improper fraction 7/4. In this case, this is the lowest form for this mixed number. However, if the mixed number is 6 4/6, then this converts to the improper fraction 40/6. One can divide the numerator and denominator of 40/6 by 2 to find that 20/3 is the lowest form for the mixed number 6 4/6.To convert a mixed number to its lowest form, one needs to change the mixed number into an improper fraction and then reduce this improper fraction to the lowest possible fraction. To do these conversions, one needs to perform a few calculations. One also has to understand the definitions of "mixed number," "improper fraction" and "proper fraction."
