Question

A football kicker can give the ball an initial speed of 24 m/s. He is 45 m from the goalpost which has a crossbar 2.69 m high.

a) What is the smallest angle of elevation that he can kick the football and score a field goal?

b) What is the largest angle of elevation that he can kick the football and score a field goal?

Answer 1

a). smallest angle, it can be 0, but if you want the ball to touch the ground only in the goalpost.

     then apply the formula = d

         so, put d = 45m v =24m/s na taking g = 10m/s2

    we get = 0.78125 implies = 25.66 degrees

____________________________________________________________________________________________

b. applying formula for hieght of a projectile at a given distance from the start.

    which gives

  

which gives 63 degrees

The formula used in part b. can be derived from

(2a)

(2b) (Trigonometric identity)

(2c) (Trigonometric identity)

(2d) (Algebra)

Let

(2e) (Substitution)

(2f) (Quadratic formula)

(2f) (Algebra)

(2g) (Substitution)