# A ball is kicked past a player who has a reaction time before he chases after the ball. The player accelerates to catch up to the ball rolling at constant speed. What is the time and distance the player has to run for after the ball passes the player?

##
During a soccer game, a ball is kicked past a player at #24.0(km)/h# . The player, who was initially at rest, has a reaction time of #0.85s# before he starts to chase after the ball. The player is able to accelerate at #1.93m/s^2# , while the ball continues to roll at constant speed.

a) How long after the ball passes the player, does the player take to catch up to the ball?

b) How far does the player have to run to catch up to the ball?

During a soccer game, a ball is kicked past a player at

a) How long after the ball passes the player, does the player take to catch up to the ball?

b) How far does the player have to run to catch up to the ball?

##### 2 Answers

#### Answer:

I get to 7.7s and 57.2m

#### Explanation:

The ball is moving ar24km//h. We need to get this into m/s:

The player has an initial speed of

The ball will have travelled a distance of

For the player, to determine the distance travelled , we can use

This has to equal the distance the ball has travelled

Combining we arrive at a quadratic equation (groan!)

Using the general formula to solve this of

Clearly t cannot be negative so the answer is 7.7s. Substituting this gives the distance the player has to run as 57m.

However, this would need the player to reach a final velocity of

#### Answer:

(a)

(b)

#### Explanation:

Let us suppose that the player takes time

1. Distance traveled by the ball in this duration

Let's change the speed from

Now

Therefore

2. Distance moved by the player after the ball passes him.

Due to his reaction time first

Using

(a) Equating (1) and (2)

Using the general expression for finding the roots of a quadratic we obtain

(b) Insert in (2)