Question

A football is kicked from the ground at an initial speed of 23 m/s at an angle of 35 degrees above the horizontal. A 3.05 m tall goal post is 45.0 m away. Find

a) Height of the ball as it crosses the goal post

b) Velocity as it crosses the goal post (speed and direction)

c) Did he make the goal? If so, by how much did he clear (vertical distance) or by how much did he miss?

d) Horizontal range of the ball (distance from kickoff to where it landed)

If you could show your work, I'd appreciate it. Thank you!

Answer 1

here ,

initial speed , u = 23 m/s

theta = 35 degree

x = 45 m

a) for the height of the ball

y = x * tan(theta) - 0.50 gx^2/(u * cos(theta))^2

y = 45 * tan(35 degree) - 0.50 * 9.8 * 45^2/(23 * cos(35 degree))^2

y = 3.55 m

the height of the ball when it crosses is 3.55 m

b)

Now, for the velocity is v

Using third equation of motion

v^2 - 23^2 = -2 * 9.8 * 3.55

v = 21.4 m/s

21.4 * cos(theta) = 23 * cos(35 degree)

theta = 28.4 degree

the velocity is 21.4 m/s at 28.4 degree below horizontal

c)

No , it didn't made the goal

distance missed = 3.55 - 3.05 = 0.50 m

distance missed is 0.50 m

d)

horizontal distance = (u^2 * sin(2 *theta))/(g)

horizontal distance = (23^2 * sin(2 * 35 degree))/9.8

horizontal distance = 50.7 m

the horizontal distance is 50.7 m