Question

A kicker aims to score a field goal in football. The kicker is 37.0 m from the tieldgoal, which is 3.05 m tall. The kicker launches the football from the ground with aninitial velocity of 29.3 m/s [41° above the horizontal]. Is a, field goal scored?

Answer 1

The field goal is scored

Step-by-step explanation:

The initial velocity is 29.3 m/s 41° above the horizontal, so the initial velocity in the horizontal and vertical direction is

`\begin{gathered} v_x=v\cos41=29.3\cos41=22.11\text{ m/s} \\ v_y=v\sin41=29.3\sin41=19.22\text{ m/s} \end{gathered}`

Now, taking into account that the kicker is 37.0 m from the field goal, we can calculate the time that football takes to reach the field goal as follows

`t=(d_x)/(v_x)=\frac{37.0\text{ m}}{22.11\text{ m/s}}=1.67\text{ s}`

Then, the height of the ball after 1.67 s is calculated as

`\begin{gathered} y=v_yt-(1)/(2)gt^2 \\ \\ y=(19.22\text{ m/s\rparen\lparen1.67 s\rparen -}(1)/(2)(9.8\text{ m/s}^2)(1.67\text{ s\rparen}^2 \\ \\ y=32.0974\text{ m - 13.66561 m} \\ y=18.43\text{ m} \end{gathered}`

Since the height of the ball is greater than 3.05 m, the field goal is scored.