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Question 823176: Please can you answer this question with all the working outs :
Nathan hits a tennis ball straight up in the air from a height of 1.25m above the ground. The ball hits the ground after 2.5 seconds assuming g=10ms-2 find
I) the speed Nathan hits the ball
II) the greatest height above the ground reached by the ball
III) the speed the ball hits the ground
IV) how high The ball bounces if it loses 0.2 of its speed on hitting the ground.
V) is your answer in part (I) likely to be over or underestimate given that you have ignored air resistance
Please can you answer these questions with all working outs thank you so much
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
a partial answer:
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equation of ballistic motion:
h(t) = -1/2gt^2 + v0t + h0
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on planet earth at the surface of the planet:
given:
g = 10 m/ss
h0 = 1.25 m
t = 2.5 sec
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h(2.5) = -5(2.5)^2 + v0(2.5) + 1.25 = 0
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-5(2.5)^2 + v0(2.5) + 1.25 = 0
v0 = ( 5(2.5)^2 - 1.25 )/2.5
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answer1:
speed Nathan hits the ball = v0 = 12 m/s
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for this problem:
h(t) = -5t^2 + 12t + 1.25 = 0
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the above quadratic equation is in standard form, with a=-5, b=12, and c=1.25
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-5 12 1.25
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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this quadratic has two real roots (the x-intercepts), which are:
t = -0.1
t = 2.5
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the quadratic vertex is a maximum at: ( t= 1.2, h(t)= 8.45 )
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negative time doesn't make sense for this problem, so use the positive root
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answer2:
the ball reaches a max height of 8.45 m (1.2 secs after being hit)
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answer3:
the ball touches the ground 2.5 seconds after being hit (this is given but confirmed by the positive root)
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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