Calculating the Velocity of a Football in Projectile Motion

Tom's Football Challenge

Tom tries to kick a football so that it stays in the air for some time. If the ball is kicked with an initial velocity of 17.9 m/s at an angle of 22.7° above the ground, what is the velocity of the ball after 3.9 s?

Final answer: To find the velocity of a football kicked in the air after a certain time, you have to calculate both horizontal and vertical components of velocity. The horizontal velocity is constant, while the vertical velocity changes due to gravity. The velocity of the football after 3.9 seconds is a vector quantity consisting of these two components.

Explanation

This problem is related to projectile motion. The initial velocity of the projectile is 17.9 m/s and the angle of projection is 22.7°. The horizontal component of velocity remains constant throughout the flight because we are ignoring air resistance. However, the vertical component of velocity changes due to gravity.

After 3.9 seconds, the horizontal component of the velocity (Vx) remains the same. It can be found by using the equation Vx = V*cos(θ) where V is initial velocity and θ is the angle of projection. The vertical component of the velocity (Vy) after 3.9 seconds can be found by using the equation Vy = V*sin(θ) - g*t where g is the acceleration due to gravity and t is time.

In this case, V is 17.9 m/s, θ is 22.7°, g is 9.8m/s², and t is 3.9 sec. Upon calculating these values you will get the velocity of the football after 3.9 seconds. The velocity of the ball after 3.9 seconds is therefore a vector quantity, made up of a horizontal (Vx) component and vertical (Vy) component. This is a classic example of a physics problem dealing with projectile motion.

Question

What is the velocity of the football after 3.9 seconds in projectile motion?

Answer

The velocity of the football after 3.9 seconds in projectile motion can be calculated by determining the horizontal and vertical components of velocity using the initial velocity, angle of projection, time, and acceleration due to gravity in the respective equations. By calculating these values, you can find the final velocity of the football after 3.9 seconds.