Projectile motion: optimal angle, landing time and location in Multivariable Calculus
In this video, we'll answer three key questions about a soccer ball kicked at 20 m/s at an angle θ: What is the optimal angle to maximize the distance the ball travels? When does the ball land? How far down the field does it land?
We analyze the projectile motion of our ball by setting up the acceleration, velocity, and position vector-valued functions. We determine the time of flight and the distance traveled as expressions depending on the angle theta. We then maximize the distance traveled as a function of theta to wrap up the answers to all three questions.
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