Question

A placekicker kicks a football at a velocity of 10.0 m/s from a tee on the ground at an angle of 30 degrees from the horizontal. Approximately how long will the ball stay in the air?

a) 0.5 seconds
b) 1.0 seconds
c) 1.5 seconds
d) 2.0 seconds

Answer 1

The football kicked at a velocity of 10.0 m/s at a 30-degree angle will remain in the air for approximately 1.0 second before it lands.

Step-by-step explanation:

The student is asking how long a football, kicked with a speed of 10.0 m/s at an angle of 30 degrees to the horizontal, will stay in the air.

To solve this, we need to consider the vertical component of the football's velocity and use the kinematic equations for projectile motion.

The vertical component (Vy) is given by Vy = V * sin(θ), where V is the initial velocity and θ is the launch angle.

Vy = 10.0 m/s * sin(30°) = 5.0 m/s

Using the equation time of flight (t) = 2 * Vy / g, where g is the acceleration due to gravity (9.8 m/s²), we can find the time the footballs stays in the air (assuming it lands at the same height it was kicked from).

t = 2 * 5.0 m/s / 9.8 m/s² ≈ 1.02 seconds.

Approximately, the football will stay in the air for about 1.0 seconds, which corresponds to option (b).