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 ?
Best Answer
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.