Asoccer player takes a free kick from a spot that is 17 m from the goal. the ball leaves his foot at an angle of 38 ∘, and it eventually hits the crossbar of the goal, which is 2.4 m from the ground. question: at what speed did the ball leave his foot?

.

Explanation:

This is a projectile motion problem, so for solving it, we will require some equations of uniform motion and free-fall.

First, we need to recognize the data that we have so we can start solving the problem.

For Free -Fall:

For uniform motion:

The time that takes to the ball to travel 17m horizontally and to hit the crossbar at 2.4m of height is the same, so time is a common variable for free-fall and uniform motion.

Using the equations:

and

and noticing that

and

,

we obtain

and

wich is a system of two equations and to variables that can be easily solve.

Making

we get

,

,

,

,

so

,

now the speed can be easily compute from one of our equations. Using

,

,

.

answer: a ball

explanation: because it will bounce

the answer is a. at the equator