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A ball is shot from a cannon into the air with an upward velocity of 36 ft/sec. The equation that gives the height (h) of the ball at any time (t) is: h(t) = -16t2 + 36t + 1.5. Find the maximum height attained by the ball.
  • a)
    21.75 ft.
  • b)
    1.125 ft.
  • c)
    1.5 ft.
  • d)
    2.25 ft.
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A ball is shot from a cannon into the air with an upward velocity of 3...
In order to find the maximum height of the ball, I would need to find the y-coordinate of the vertex.
Vertex formula: x = - b/2a
where: a = -16 b = 36 c = 1.5

x = 1.125
Now substitute 1.125 for t into the equation and solve for h(t). H(t) = -16 (1.125)2 + 36 (1.125) + 1.5
H(t) = 21.75
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Community Answer
A ball is shot from a cannon into the air with an upward velocity of 3...
Understanding the Height Equation
The height of the ball is described by the quadratic equation:
h(t) = -16t² + 36t + 1.5

This equation represents a parabola that opens downwards, indicating that the ball will reach a maximum height before falling back down.
Finding the Maximum Height
To find the maximum height, we can use the vertex formula of a quadratic equation. The time (t) at which the maximum height occurs can be found using:
t = -b / (2a)

where:
- a = -16 (coefficient of t²)
- b = 36 (coefficient of t)
Calculating Time of Maximum Height
Substituting the values into the formula:
t = -36 / (2 * -16)

t = -36 / -32

t = 1.125 seconds

This is the time at which the maximum height is reached.
Calculating Maximum Height
Now, substitute t back into the height equation to find h(1.125):
h(1.125) = -16(1.125)² + 36(1.125) + 1.5

h(1.125) = -16(1.265625) + 40.5 + 1.5

h(1.125) = -20.25 + 40.5 + 1.5

h(1.125) = 21.75 ft

Conclusion
The maximum height attained by the ball is:
21.75 ft

Thus, the correct answer is option 'A'.
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A ball is shot from a cannon into the air with an upward velocity of 36 ft/sec. The equation that gives the height (h) of the ball at any time (t) is: h(t) = -16t2 + 36t + 1.5. Find the maximum height attained by the ball.a)21.75 ft.b)1.125 ft.c)1.5 ft.d)2.25 ft.Correct answer is option 'A'. Can you explain this answer?
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A ball is shot from a cannon into the air with an upward velocity of 36 ft/sec. The equation that gives the height (h) of the ball at any time (t) is: h(t) = -16t2 + 36t + 1.5. Find the maximum height attained by the ball.a)21.75 ft.b)1.125 ft.c)1.5 ft.d)2.25 ft.Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A ball is shot from a cannon into the air with an upward velocity of 36 ft/sec. The equation that gives the height (h) of the ball at any time (t) is: h(t) = -16t2 + 36t + 1.5. Find the maximum height attained by the ball.a)21.75 ft.b)1.125 ft.c)1.5 ft.d)2.25 ft.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball is shot from a cannon into the air with an upward velocity of 36 ft/sec. The equation that gives the height (h) of the ball at any time (t) is: h(t) = -16t2 + 36t + 1.5. Find the maximum height attained by the ball.a)21.75 ft.b)1.125 ft.c)1.5 ft.d)2.25 ft.Correct answer is option 'A'. Can you explain this answer?.
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