Question

Johnny kicked a football from a hill 20 meters tall. The ball leaves at a 45.0 degree angle with an initial velocity of 30.0 m/second. How many seconds was the ball in the air? Report your answer to 3 sig figs. Seconds

Answer 1

Answer:

The value is $t = 5.124 \ s$

Explanation:

From the question we are told that

   The height of the tree is $s = 20 \ m$

    The angle the ball leaves is  $\theta = 45^o$

    The initial velocity  is  $u = 30.0 \ m/s$

Generally the vertical of the ball's initial velocity is mathematically evaluated as

      $u_y = u * sin (45)$

=>   $u_y =- 30 * sin (45)$

=>   $u_y = -21.21 \ m/s$

Here  $u_y$ is negative because it is in the direction of the negative y-axis

Generally from kinematic equation we have

      $s = u_yt + \frac{1}{2} g t^2$

=>   $20= -21.21 t +4.9 t^2$

=>   $4.9 t^2 -21.21 t- 20= 0$

Solving using quadratic formula we have that

        $t = 5.124 \ s$