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

The value is
`t = 5.124 \ s`

Step-by-step 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 + (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`