a. Explanation Given: An object is launched from an origin with an initial speed | v 0 | at an angle α to the horizantal direction for 0 ≤ θ ≤ π 2 and the trajectory if the ground slopes downward at a constant angle of θ from the launch site. Definition used: Let the position vector of an object moving in two dimensional space be given by r ( t ) = 〈 x ( t ) , y ( t ) 〉 for t ≥ 0 . Then velocity of the object v ( t ) is the derivative of the position vector, r ′ ( t ) = 〈 x ′ ( t ) , y ′ ( t ) 〉 . Then, the position vector can be obtained from antiderivative of velocity vector as r ( t ) = ∫ ( v ( t ) ) d t . Calculation: Let the velocity can be given by 〈 v 0 cos α , v 0 sin α − g t 〉 where x -axis is horizantal along the ground with initial velocity s and y -axis is in vertical direction with initial velocity s and has the gravity for g . Compute the antiderivative of velocity vector v ( t ) = 〈 v 0 cos α , v 0 sin α − g t 〉 as follows, r ( t ) = ∫ v ( t ) d t = ∫ 〈 v 0 cos α , v 0 sin α − g t 〉 d t = 〈 v 0 t cos α , v 0 t sin α − g t 2 2 〉 Thus, the position vector of the ball hits the hole is r ( t ) = 〈 v 0 t cos α , v 0 t sin α − g t 2 2 〉 . Let us assume t = T as a time of flight. Compare the position vector r ( t ) = 〈 v 0 T cos α , v 0 T sin α − g T 2 2 〉 with the point ( a , − a tan θ ) to the equations, a = v 0 T cos α (1) − a tan θ = v 0 T sin α − g T 2 2 (2) Substitute a = v 0 T cos α in the equation (2) b. To determine To find: The time of flight, range and maximum height of the trajectory.

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ISBN: 9781323178522

Author: Briggs

Publisher: PEARSON

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Chapter 11.7, Problem 76E

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To find: The time of flight, range and maximum height of the trajectory.

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To find: The time of flight, range and maximum height of the trajectory.

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Chapter 11.7, Problem 75E

Chapter 11.7, Problem 77E

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The time of flight, range and maximum height of the trajectory.

Solution Summary: The author explains that the time of flight, range and maximum height of the trajectory are 2v_0g(mathrm

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To find: The time of flight, range and maximum height of the trajectory.

To find: The time of flight, range and maximum height of the trajectory.

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