Question

A football is kicked with an initial velocity of 25 m/s at an angle of 45 degrees with the horizontal. Determine how long it takes for the ball to hit the ground.

A. 1.83 seconds
B. 2.00 seconds
C. 2.50 seconds
D. 3.00 seconds

Answer 1

is B. 2.00 seconds. the time \(t\) is found to be approximately 2.00 seconds. This time represents the duration it takes for the football to return to the ground after being kicked.

Explanation

When a football is kicked with an initial velocity of 25 m/s at an angle of 45 degrees, the time it takes for the ball to hit the ground can be calculated using the equations of motion.

By breaking the initial velocity into its horizontal and vertical components, we find that the initial vertical velocity is
`\(V_(i_y) = V_i * \sin(\theta)\),` where \(V_i\) is the initial velocity (25 m/s) and
`\(\theta\)`is the angle (45 degrees). Given that the vertical acceleration due to gravity is -9.81 m/s², we can employ the kinematic equation
`\(s = V_(i_y) * t + (1)/(2) * a * t^2\)` to solve for time. Substituting the values, the time \(t\) is found to be approximately 2.00 seconds. This time represents the duration it takes for the football to return to the ground after being kicked.

Understanding the components of the initial velocity, the influence of gravity, and applying the kinematic equation for vertical motion helps determine the time taken for the football to hit the ground when kicked at an angle. The time calculated provides a precise estimation of the duration of flight before the football descends back to the ground.