Question

A soccer field is viewed from above, while a ball is kicked eastward with an initial speed of 10.0 m/s. The ball experiences a constant eastward acceleration of 0.75 m/s 2 over a distance of 20.0 m. Immediately after this 20.0 m distance, the ball is kicked northward in a manner that does not change its speed at that point, just its direction. The ball is allowed to come to a complete stop. How far north does the ball travel before stopping if the acceleration after this kick is 1.15 m/s 2

Answer 1

Answer:

the ball travelled approximately 60 m towards north before stopping

Explanation:

 Given the data in the question;

First course : $a_{x}$ = 0.75 m/s², $d_{x}$ = 20 m, $u_{x}$ = 10 m/s

now, form the third equation of motion;

v² = u² + 2as

we substitute

$v_{x}$² = (10)² + (2 × 0.75 × 20)

$v_{x}$² = 100 + 30

$v_{x}$² = 130

$v_{x}$ = √130

$v_{x}$ = 11.4 m/s

for the Second Course:

$u_{y}$ =  11.4 m/s,  $a_{y}$ = -1.15 m/s²,  $v_{y}$ = 0

Also, form the third equation of motion;

v² = u² + 2as

we substitute

0² = (11.4)² + (2 × (-1.15) ×  $d_{y}$ )

0 = 129.96 - 2.3$d_{y}$

2.3$d_{y}$  = 129.96

$d_{y}$ = 129.96 / 2.3

$d_{y}$ = 56.5 m

so;

|d| = √( $d_{x}$² + $d_{y}$² )

we substitute

|d| = √( (20)² + (56.5)² )

|d| = √( 400 + 3192.25 )

|d| = √( 3592.25 )

|d| = 59.9 m ≈ 60 m

Therefore, the ball travelled approximately 60 m towards north before stopping