Final answer:
The question asks about the time a football remains in the air after being kicked at an angle with a given initial velocity. To find this, one must calculate the initial vertical velocity and use kinematic equations to solve for the time it takes for the football to land.
Step-by-step explanation:
The student's question pertains to projectile motion, a concept in physics. When calculating the total time a football is in the air after being punted, it's crucial to consider the vertical motion independently from the horizontal motion, as they are independent of each other in projectile motion.
First, we need to calculate the initial vertical velocity (v_yi) using the provided initial speed v_i and the angle θ:
v_yi =
v_i * sin(θ)
Subsequently, we can determine the time t the football spends in the air by using the kinematic equation for vertical motion:
0 =
v_yi *
t - ½ *
g *
t²
Where g is the acceleration due to gravity (9.81 m/s²). Given that t = 0 when the ball is kicked, we can solve for the second root of the equation for the time the ball lands back to the ground. Reaching this point, the student should be able to perform the necessary calculations to find the correct time interval after which the ball returns to the ground.