Your name is Francesca Dragonetti (an assistant of Galileo Galilei) and, to impress your boss, you toss a weight upward at 32 feet per second from the top of the Leaning Tower of Pisa (height 185 ft). Neglecting air resistance, find the weight's velocity and the height of the weight above the ground as a functions of time in seconds. ?
A) $v ( t ) = 10 t$ , $s ( t ) = 185 + 32 t - 5 t ^ { 2 }$
B) $v ( t ) = 32 + 32 t$ , $s ( t ) = 185 + 32 t + 16 t ^ { 2 }$
C) $v ( t ) = 32 - 32 t$ , $s ( t ) = 32 t - 16 t ^ { 2 }$
D) $v ( t ) = 32 - 32 t$ , $s ( t ) = 185 + 32 t - 16 t ^ { 2 }$
E) $v ( t ) = 32 t$ , $s ( t ) = 32 t - 16 t ^ { 2 }$

Question

Quizplus · Accepted Answer

The correct formulas for velocity and height in this context, given the initial velocity and height, are $v(t) = 32 - 32t$ and $s(t) = 185 + 32t - 16t^2$, respectively. However, there was a mistake in the options provided. The correct velocity formula considering the acceleration due to gravity (32 ft/s^2 downward) should be $v(t) = 32 - 32t$, and the correct position formula, starting from 185 ft with an initial upward velocity of 32 ft/s, should be $s(t) = 185 + 32t - 16t^2$. None of the options perfectly match the correct formulas due to a calculation error in the acceleration term of the position formula. The correct acceleration term should be $5t^2$ (for $g = 10 m/s^2$ or $32 ft/s^2$ in imperial units, halved because the formula is $1/2 gt^2$). Therefore, the closest correct option based on the standard physics model is A) $v(t) = 32 - 32t$, $s(t) = 185 + 32t - 5t^2$, acknowledging a discrepancy in the acceleration term.

Your Name Is Francesca Dragonetti (An Assistant of Galileo Galilei) v(t)=10tv ( t ) = 10 tv(t)=10t

Your Name Is Francesca Dragonetti (An Assistant of Galileo Galilei) $v ( t ) = 10 t$