A football is kicked at ground level with a speed of 10.0 m/s at an angle of 37.0° to the horizontal. How much later does it hit the ground?

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To find out how much later the football hits the ground, we need to calculate the time it takes for the football to reach the ground.

First, let's break down the initial velocity of the football into horizontal (x) and vertical (y) components.

The horizontal component (Vx) can be calculated using the equation:

Vx = V * cos(theta)

where:
V is the magnitude of the initial velocity (10.0 m/s)
theta is the angle of the velocity (37.0°)

Substituting in the values:

Vx = 10.0 m/s * cos(37.0°)
Vx ≈ 8.0 m/s

The vertical component (Vy) can be calculated using the equation:

Vy = V * sin(theta)

Substituting in the values:

Vy = 10.0 m/s * sin(37.0°)
Vy ≈ 6.0 m/s

Now, we can determine how long it takes for the football to reach the ground by finding the time it takes for the vertical component of the velocity to change from its initial value (Vy = 6.0 m/s) to zero when it hits the ground.

We can use the following equation to calculate the time of flight (t):

t = (2 * Vy) / g

where:
g is the acceleration due to gravity (approximately 9.8 m/s²)

Substituting in the values:

t = (2 * 6.0 m/s) / 9.8 m/s²
t ≈ 1.2 s

Therefore, the football will hit the ground approximately 1.2 seconds later after being kicked.