A placekicker is about to kick a field goal. The ball is 20.1 m from the goalpost. The ball is kicked with an initial velocity of 18.7 m/s at an angle θ above the ground. Between what two angles, θ1 and θ2, will the ball clear the 3.12-m-high crossbar? Give your answers as (a) the smaller angle and (b) the larger angle. (Hint: The following trigonometric identities may be useful:

Question

A placekicker is about to kick a field goal. The ball is 20.1 m from the goalpost. The ball is kicked with an initial velocity of 18.7 m/s at an angle θ above the ground. Between what two angles, θ1 and θ2, will the ball clear the 3.12-m-high crossbar? Give your answers as (a) the smaller angle and (b) the larger angle. (Hint: The following trigonometric identities may be useful:
sec θ = 1/(cos θ) and sec2θ = 1 + tan2θ.)