Question

1. which situations in problem 3 represent projectile motion? 5. a ball is dropped from a height of 10 meters. conor and evan write equations for functions to model the situation where t is time in seconds. conors function is defined by a(t)=10 - 5t². evans function is defined by b(t)=5t². do you agree with either persons selected model? explain. 6. the function h models the height of a flower - pot after it falls off a balcony. the table shows the height in feet of the flower - pot after it starts to fall. time (seconds) 0 0.5 1 1.5 2 height (feet) 64 60 48 28 0 which equation gives the height h(t) in feet of the flower - pot t seconds after it falls off the balcony? a. h(t)=64 - 4t² b. h(t)=64 - 16t c. h(t)=64 - 16t² d. h(t)=64 - 4t

Explanation:

Step1: Recall the free - fall height formula

The height of an object in free - fall (neglecting air resistance) is given by $h(t)=h_0 - \frac{1}{2}gt^2$, where $h_0$ is the initial height and $g$ is the acceleration due to gravity. On Earth, $g\approx 32$ ft/s² in English units and $g = 10$ m/s² in SI units.

Step2: Analyze the ball - dropping situation in problem 5

The ball is dropped from a height of $h_0 = 10$ meters. Using the formula $h(t)=h_0-\frac{1}{2}gt^2$ with $g = 10$ m/s², we have $h(t)=10-\frac{1}{2}\times10t^2=10 - 5t^2$. So Conor's function is correct.

Step3: Analyze the flower - pot situation in problem 6

The initial height of the flower - pot is $h_0 = 64$ feet. Using the formula $h(t)=h_0-\frac{1}{2}gt^2$ with $g = 32$ ft/s², we get $h(t)=64-\frac{1}{2}\times32t^2=64 - 16t^2$.

Answer:

For problem 5: I agree with Conor's selected model because the height of an object in free - fall from an initial height $h_0$ is $h(t)=h_0-\frac{1}{2}gt^2$, and with $h_0 = 10$ m and $g = 10$ m/s², $h(t)=10 - 5t^2$.
For problem 6: C. $h(t)=64 - 16t^2$