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I have the question ``A football is kicked at a speed of 20 $m/s$ at and angle of 45 degrees. (Assume negligible air resistance). Calculate the time taken for the ball to reach its maximum height''

I know from the previous question that the vertical and horizontal components of the initial velocity is 14.14 $m/s$.

I also know that the velocity is 0 at the maximum height and the acceleration is -9.81 as we are going against gravity.

I rearranged the equation of $v = v_0 + at$ to find the value of $t$ which is 2.88 seconds and then halved this to get t = 1.44 $s$.

Is this correct ? If not can be explain where I went wrong ?

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    $\begingroup$ Yes, your answer is correct. $\endgroup$ – jcandy Oct 18 '17 at 20:26
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    $\begingroup$ The answer is $10\sqrt{2}/9.81$, which is obtained using $0=u + at$. It does not make any sense to calculate the whole time of flight first. $\endgroup$ – Math Lover Oct 18 '17 at 20:28
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The equation of an object's displacement with the ground is the following: $$y= y_0 + v_0 t -\frac12 (9.81) t^2$$

Which would mean that it's velocity at time $t$ would be $$v(t) = v_0 -9.81t$$

You have correctly figured out that the initial velocity in the vertical direction is $14.14$. You also seemed to figure out that the vertical velocity would be $0$ at the maximum height.

So we have to solve the following equation: $$0=14.14-9.81t$$

Solving for $t$ gives us $t \approx 1.4 414$

There shouldn't be any need to divide anything in half in this situation.

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