Final answer:
With the starting velocity and acceleration due to gravity known, we can compute the horizontal and vertical displacements to find the position of the ball at 1.2 seconds. The ball's maximum height can be calculated from its initial vertical velocity and its acceleration as a result of gravity. We may multiply the time it takes the ball to reach the ground by its horizontal velocity to determine where it lands.
Step-by-step explanation:
a) Where will the ball be 1.2 seconds after it is kicked?
We may take into account the ball's independent motion in both the horizontal and vertical directions to calculate its displacements after 1.2 seconds. We are aware that there is no horizontal acceleration and that the starting velocity for the horizontal motion is 25 m/s. Consequently, the following formula can be used to determine the ball's horizontal displacement after 1.2 seconds:
horizontal displacement = (initial velocity)(time) = (25 m/s)(1.2 s)
For the vertical motion, we know that the initial vertical velocity is 12 m/s and the acceleration due to gravity is -9.8 m/s² (negative because it acts opposite to the positive direction). Using the formula for vertical displacement, we can calculate the vertical displacement of the ball after 1.2 seconds:
vertical displacement = (initial vertical velocity)(time) + (1/2)(acceleration)(time^2) = (12 m/s)(1.2 s) + (1/2)(-9.8 m/s²)(1.2 s)^2
By calculating these displacements, we can determine the coordinates of the ball at 1.2 seconds.
b) What will be the greatest height reached by the ball?
For the vertical motion, we know that the initial vertical velocity is 12 m/s and the acceleration due to gravity is -9.8 m/s². To find the maximum height, we can use the formula:
maximum height = (initial vertical velocity)^2 / (2)(acceleration) = (12 m/s)^2 / (2)(-9.8 m/s²)
By calculating this, we can determine the greatest height reached by the ball.
c) Where will the ball land?
To determine where the ball will land, we need to calculate the total time of flight of the ball. Using the formula for vertical motion, we can find the time it takes for the ball to reach the ground:
0 = (initial vertical velocity)(time) + (1/2)(acceleration)(time^2)
By solving this equation, we can find the time it takes for the ball to reach the ground. Then, by multiplying this time by the horizontal velocity of the ball, we can find the horizontal distance traveled by the ball. This will give us the location where the ball lands.