## Sports Mathematics

Mathematics is prevalent in all aspects of our lives from the grocery to the mechanic shop and from the classroom
to the playing field. In this section, we'll discuss how mathematics is applied in the field of sports. Let's take a look at
the examples below:

#### Example 1

A basketball player shoots a basketball from his hand at an initial height of 1 m with an initial upward velocity of 10
meters per second. What is the equation to represent the height of the ball after 2 seconds? The quadratic equation to represent a parabola is y = ax2 + b x + c. In this problem, write the equation as h=0.5 a
t2+ut where t is time in seconds,' a' is the acceleration and u is the initial velocity with which the ball is thrown and h
is the height of the basket.

#### Example 2

The number of balls faced by a batsman is 50 and the runs scored by him are 100. Find the strike rate given that
strike rate is the runs scored by the batsman per 100 balls faced.

 Runs scored for 50 balls = 100 Represent runs scored per ball as x 1. Runs scored for 1 ball = 100/50 = 2 x = 100/50 2. Strike rate = runs scored for 100 balls = 200 Represent strike rate with s, then s = 100x = 200

#### Example 3

A batsman has scored 200 runs in 14 overs. Calculate his run rate per over given that

run rate = runs scored / overs.

Step 1 Run rate = runs scored/ overs

Let run rate = r, runs scored = x and overs = o

Step 2 Run rate = 200/14 = 14.28

Then r = x/o = 200/14 = 14.28

#### Try these questions

1. Lenny drives his bike the first 3 hours of his journey at 12 mph speed and the remaining 5 hours at 10 mph speed. What is the average speed of Jim's travel in mph?

1. 12 mph

2. 8 mph

3. 10.75 mph

4. 12.5 mph

5. 11 mph

#### Explanation

Average speed = Total distance traveled by Lenny = Distance covered in the first 3 hours + Distance covered in the next 5 hours.

Distance covered in the first 3 hours = 3 * 12 = 36 miles

Distance covered in the next 5 hours = 5 * 10 = 50 miles

Therefore, total distance traveled = 36 + 50 = 86 miles.

Total time taken = 3 + 5 = 8 hours.

Average speed = 86 / 8 = 10.75 mph.