Mathematics
Grade10
Easy
Question
Write a quadratic function for the maximum height, if the initial velocity is 150
, the initial height is 30 ft.
- 30t + 150
- 0
Hint:
At maximum height the velocity becomes momentarily zero.
The correct answer is: ![negative 16 t squared plus 150 t plus 30](data:image/png;base64,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)
The height of the shot (vertical motion model) = ![negative 16 t squared plus v subscript 0 t plus h subscript 0](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH0AAAAVCAYAAABrJ+ESAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAApVJREFUeNrtWUFEREEYfrJWViLpkA6RtVaSLkmSLh2SJJGkU6JD0rVTundI0iVJksQekqRLkpUkkqwO6d6hS7KSrNj+4UuvMfPezNvZ3tve+/h4b/a9ed////PP/DNrWZWBIlggXhKTVoTQoIo4S7yNXBE+fEQuCBf6iNnIDf4iRVwk3rk810nMEPPI1CMEUAeNWNNbQu7zdyx1vmGXOINCS4YZBDmF+1riJPGCey6JoMoG1zECH2Q42WCq/1yQKmwRWok3in2MEvckGX6CwWJKV7kgs8GUxhHiftCDvkGcUHh/ybY1Y1yw/cYCnjasSzVYZ8RBxT6cbDAV9CX0W09cIT4TX4jzQQr6g8aUnMFIlu3T7TQd9KSgLmE1x7WmH2Q2mAp6BoFnS+Mw1vYm1EmJoAT9A+vxAQqQAqb7SckAaf4jXSoF0hWxX/N7XmzQ0fiI2qaGa39B9mt/2I1ehBdxmMKmyBic2gPxs9zBy7uhIHu1gwW5HdcDHraGqjZ41cj6fxNkdMyQ74xlVB7TD48O4pPtvqtM+2+dLNohjuGaTfXdmt/yakNRo/8zQTvTeR6koJ847CkLtusJON3PoLOZZxlr8qnkmSFM4Q+4tgzYoKqR9b+t0e6ktazOZY4cF7SnuSJplTjnc9AHUXvcYyYSZVQWa2c9sqvbgA2qGteIU5L2aU2tZXVuHB+fxtrzPU3luCJpnbjlc9AT1s9poQiH1u9TxF7uWa82qGo8kGwfRe1uWo0XTjwaiJsoQj4xCHoFhzhPeD/u43nDK7HNoT6p4gqr/B/awCr0asV2N60RSsjIQqT1f4PPnliAs6eStAYa/DrZh4OSSOs/xvd+uA51StZSP5ePtFYw2H730fLxT45StX4BB1jVOFQ1ljEAAADcdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTY8L21uPjxtc3VwPjxtaT50PC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bXN1Yj48bWk+djwvbWk+PG1uPjA8L21uPjwvbXN1Yj48bWk+dDwvbWk+PG1vPis8L21vPjxtc3ViPjxtaT5oPC9taT48bW4+MDwvbW4+PC9tc3ViPjwvbWF0aD4aoA9bAAAAAElFTkSuQmCC)
![equals negative 16 t squared plus 150 cross times t plus 30](data:image/png;base64,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)
![equals negative 16 t squared plus 150 t plus 30](data:image/png;base64,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)
Hence, the correct option is D.
We have, h = ut - 1/2gt².
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