A football kicker can give the ball an initial speed of 26 m/s. What are the (a)

Question

A football kicker can give the ball an initial speed of 26 m/s. What are the (a) least and (b) greatest elevation angles at which he can kick the ball to score a field goal from a point 44 m in front of goalposts whose horizontal bar is 3.44 m above the ground?

Explanation / Answer

When he kicks, the velocity is partly horizontal and partly vertical. Vertical vv = v.sin(a) with a is angle between ground and initial velocity. vx = v.cos(a) is the horizontal velocity at that time t the vertical distance must be over 3.21 m so v.sin(a).t - (1/2).9.81.t² > 3.21 -4.905.t² + 25.sin(a).t - 3.21 > 0 This is a parabola with a top. At this time the horizontal displacement must be 44 = 25.cos(a).t so: -4.905.(44/25.cos(a))² + 25.sin(a).(44/25.cos(a)) - 3.21 = 0 gives the 0 points. multiply this by cos²(a) -4.905.(44/25)² + 25.sin(a).cos(a).(44/25) - 3.21.cos²(a) = 0 sin(a).cos(a) = sin(2a)/2 cos²(a) - sin²(a) = cos(2a) => 2.cos²(a) -1 = cos(2a) -16.80 + 22.sin(2a) - 1.605.cos(2a) = 0 {-16.80 + 22.sin(2a)}² = 1.605.(1 - sin²(2a)) 482.4.sin²(2a) - 739.2.sin(2a) + 280.6 = 0 sin(2a) = + 0.766 +/- 0.073 a = (21.9 degrees and) 68.1 degrees a = 28.5 degrees (and 61.5 degrees)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.