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Projectile in 2D: A ball is thrown with initial speed V , at an angle θ...

Projectile in 2D: A ball is thrown with initial speed V , at an angle θ above the horizontal, over flat ground. Show that the motion is restricted to a single plane. Neglecting air resistance, find (a) the time taken for the ball to reach the ground; (b) the maximum height reached by the ball; (c) the horizontal distance travelled by the ball before hitting the ground (range); (d) the kinetic and potential energies at the position of maximum height (and verify that their sum equals the initial energy). The following are experimental data on the range and muzzle velocity of mortar shells, all fired at 45◦ to the horizontal. The time of flight is also tabulated. Compare the ranges and times with the simple treatment above. How would you explain any differences?

Muzzle Velocity (m/s) Range (m) Time (s)

101.8 972 14.4

112.2 1160 15.7

121.9 1349 17.0

131.4 1539 18.2

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