Maximizing Distance for Clowns Shot from a Cannon

AI Thread Summary
The maximum distance a clown can travel when shot from a cannon at a speed of 11.7 m/s, with the landing pad at the same height, is determined by the launch angle. For optimal distance, the angle should be 45 degrees, yielding a maximum distance D. To have two clowns land simultaneously at a distance of 0.54×D, the first clown should be fired at a specific angle, while the second clown must be fired at a different angle to account for the timing. The discussion emphasizes the need for calculations to determine these angles and the timing of the second clown's launch. Accurate projectile motion equations are essential for solving these problems effectively.
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In a circus act, clowns are shot from a cannon at a constant speed vo = 11.7 m/s. The angle of launch may be varied.

a. What is the maximum distance D that a clown may travel, if the landing pad is at the same height as the mouth of the cannon?

b. The circus master wants to shoot two clowns from his cannon, one after the other, and have them land on the same landing pad a distance 0.54×D away at the same time. At what angle should the first clown be fired?

c. At what angle should the second clown be fired?

d. How long after the first clown should the second clown be fired?
 
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