Final answer:
The horizontal and vertical components of a football kicked at an angle are determined by the cosine and sine of that angle multiplied by the initial velocity, respectively. The time it is airborne is computed using the vertical component and the acceleration due to gravity. The horizontal distance is the product of the time in the air and the horizontal component of velocity.
Step-by-step explanation:
When a football is kicked with a speed of 18m/s at an angle of 65 degrees to the horizontal, we can find the horizontal and vertical components of the initial velocity using trigonometry. The horizontal component (Vx) is found by multiplying the initial velocity by the cosine of the angle, and the vertical component (Vy) is found by multiplying by the sine of the angle. Therefore, Vx = 18m/s * cos(65) and Vy = 18m/s * sin(65).
To determine how long the football is in the air, we can use the vertical motion equations under gravity. Since the vertical motion is symmetrical and the football returns to the same level it was kicked from, the time in the air is twice the time taken to reach the highest point, which can be calculated as Vy / g, where g is the acceleration due to gravity (approximately 9.81 m/s²).
The horizontal distance traveled by the football before it hits the ground (also called the range) is found by multiplying the horizontal component of velocity (Vx) by the time the football is in the air.