A Baseball Slugger Hits a Knee-High Pitch Toward the Outfield $o$

question 85

Essay

A baseball slugger hits a knee-high pitch toward the outfield. Suppose that the position of the baseball after t seconds is given by :
x = (v $o$ cos $\alpha$ ) t, y = (v $o$ sin $\alpha$ ) t $- 16 t ^ { 2 } + h _ { o }$ where v $o$ is the velocity in feet per second at which the ball leaves the bat at an angle $\alpha$ to the horizontal and from a height h $o$ above the ground.(a) Suppose that the ball is struck 2 feet above the ground with an initial velocity of 120 ft/sec and at an angle of 35 degrees.(i) When will the ball strike the ground?
(ii) How far will the ball travel (horizontally) before it touches the ground?
(iii) What is the maximum height reached by the ball?
(iv) Will the ball clear the 10 ft tall outfield fence, which is 410 feet away from the point where the ball is struck?
(b) If the ball is struck 2 feet above the ground at an initial velocity of 120 ft/sec and at an angle of 55 degrees:
(i) When will the ball strike the ground?
(ii) How far will the ball travel (horizontally) before it touches the ground?
(iii) What is the maximum height reached by the ball?
(iv) Will the ball clear the 10' tall outfield fence, which is 410 feet away from the point where the ball is struck?

Comprehend the concepts of liquidity and how it affects financial decisions.

Understand the impact of interest rates on the economy and individual financial planning.

Grasp basic principles of inflation and its effects on financial planning and the economy.

Learn the significance of consumer spending and its effects on the economy.

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Definitions:

Cognitive Dissonance

The mental discomfort experienced by a person who holds two or more contradictory beliefs, ideas, or values at the same time.

Relationship Satisfaction

The degree of contentment and fulfilment one feels in their romantic partnership, often influenced by communication, emotional support, and shared values.

Equity

The principle of fairness and impartiality, often applied in the context of law, finance, and social justice.

Psychological Exchange Theory

A social psychology concept suggesting that interpersonal relationships are formed and maintained based on perceived rewards and costs, mutual benefits, and fairness.