(a) The maximum height of the ball above the ground is 12.5 m and the time of motion is 1.43 s.
(b) The time taken for the ball to contact the other player at 0.5 m above the ground is 3.0 s.
<h3>Maximum height reached by the ball</h3>
The maximum height reached by the ball is calculated as follows.
At maximum height, the final velocity, v = 0
dh/dt = v = 0
dh/dt = -2(4.9)t + 14
0 = -9.8t + 14
9.8t = 14
t = 1.43 s
H(1.43) = -4.9(1.43)² + 14(1.43) + 2.5
H(1.43) = -10.02 + 20.02 + 2.5
H(1.43) = 12.5 m
<h3>Time to reach maximum height</h3>
12.5 = -4.9t² + 14t + 2.5
4.9t² - 14t + 10 = 0
t = 1.43 s
<h3>Time for the ball to reach 0.5 m above the ground</h3>
0.5 = -4.9t² + 14t + 2.5
4.9t² - 14t + - 2 = 0
t = 3.0 seconds
The complete question is below:
In a volleyball match Hanein serves the volleyball at 14 m/s, from a height of 2.5 m above the court. The height of the ball in flight is estimated using the equation, h = -4.9t² + 14t + 2.5, where t is the time in second and h is height above ground, in metres.
Learn more about time of motion here: brainly.com/question/2364404
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Answer: The required matrix is
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Step-by-step explanation: The given linear transformation is
T(f(t)) = 4f'(t) + 6f(t).
We are to find the matrix A of T from P² to P² with respect to the standard basis P² = {1, t, t²}.
We have
Therefore, the matrix A is given by
Thus, the required matrix is
Answer: The fact that beyblades spin at different speeds, you may want to get one that is fast while staying in control. Some have more mass than others leading them to spin slower, but the fact that they weigh so much may cause the other one to richochet off of it. Therefore get a big but fast beyblade that is very stable.
Future Value = Present Value*(1 + interest rate)^(# of years)
Future Value = $2,000(1+0.08)^1
Future Value = $2,000(1.08) = $2,160
To find the interest on the loan, we need to do our Future Value - Present Value.
Future Value - Present Value = $2,160 - $2,000 = $160
Answer:
x = 4/7
y = 60/7
Step-by-step explanation:
3x + 4y = 36
y = x + 8
Substitute the second equation into the first since it already has the y isolated for you:
3x + 4(x + 8) = 36
3x + 4x + 32 = 36
7x = 4
x = 4/7
Take the answer you got from the equation above and plug that into the second equation:
y = 4/7 + 8
y = 60/7
To check just LS/RS both equations:
3(4/7) + 4(60/7) = 36
12/7 = 240/7 = 36
252/7 = 36
36 = 36
LS = RS
60/7 = 4/7 + 8
60/7 = 60/7
LS = RS
