EXAMPLE 6 A projectile is fired with muzzle speed 220 m/s and an angle of elevation 45° from a position 20 m above groun

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Example 6 A Projectile Is Fired With Muzzle Speed 220 M S And An Angle Of Elevation 45 From A Position 20 M Above Groun 1 (59.86 KiB) Viewed 24 times

EXAMPLE 6 A projectile is fired with muzzle speed 220 m/s and an angle of elevation 45° from a position 20 m above ground level. Where does the projectile hit the ground and with what speed? SOLUTION If we place the origin at ground level, then the initial position of the projectile is (0, 20) and so we need to adjust the parametric equations of the trajectory by adding 20 to the expression for y. With Vo = 220 m/s, a = 45°, and g = 9.8 m/s2, we have x = 220 cos(1/4)t = x y = 20 + 220 sin(5/4)t - 2(9.8)2 = Impact occurs when y = 0, that is 4.962 - 110/2t - 20 = 0. Solving this quadratic equation (and using only the positive value of t), we get the following. (Round your answer to two decimal places.) 110V2 + 24,200 + 392 9.8 Then x = 110/2(31.88) (rounded to the nearest whole number), so the projectile hits the ground about m away. The velocity of the projectile is v(t) r'(t) = So its speed at impact (rounded to the nearest whole number) is IV(31.88)1 = (1102)2 + (110V2 - 9.8. 31.88)2 = = m/s.