Question

(distance between the two-goal lines on the football ground is 100 yards) A football player runs from his own goal line to the opposing teams goal line, returning to his thirty-yard line, all in 25.5 s. Calculate his average speed and the magnitude of his average velocity. (Enter your answers in yards/s.) A) calculate his average speed. B) calculate the magnitude of his average velocity.

Answer 1

Given data:

* The distance between the two-goal lines on the football ground is d = 100 yards.

* The player covered the distance while returning is,

`\begin{gathered} d^(\prime)=100-30 \\ d^(\prime)=70\text{ yards} \end{gathered}`

* The time taken by the player in the complete run is t = 25.5 s.

Solution:

(A). The distance traveled by the player during the complete run is,

`\begin{gathered} D=d+d^(\prime) \\ D=100+70 \\ D=170\text{ yards} \end{gathered}`

The average speed of the player is,

`\begin{gathered} s=(D)/(t) \\ s=(170)/(25.5) \\ s=6.67\text{ yards/s} \end{gathered}`

Thus, the average speed of the player is 6.67 yards/second.

(B). The displacement of the player is,

`D^(\prime)=d-d^(\prime)`

Here, the negative sign is indicating the direction of motion of the player while the return is opposite to the initial direction of motion.

Substituting the known values,

`\begin{gathered} D^(\prime)=100-70 \\ D^(\prime)=30\text{ yards} \end{gathered}`

The average velocity of the player is,

`\begin{gathered} v=(D^(\prime))/(t) \\ v=(30)/(25.5) \\ v=1.2\text{ yards/s} \end{gathered}`

Thus, the average velocity of the player is 1.2 yards/second.