Question

free fall practice

1. a model rocket is launched straight upward at 58.8 m/s.

a. how long does it take for the rocket to reach its peak height?
given\tunknown\tequation\tsubstitution\tanswer & units
δy =
vf =
a =
t =
a. what is the peak height of the rocket from the ground?
given\tunknown\tequation\tsubstitution\tanswer & units
δy =
vf =
a =
t =

1. in a class experiment to determine information about free - fall acceleration, a watermelon and a pumpkin are each set to fall from the back of the stands at your football stadium.

a. if the watermelon and the pumpkin are both dropped at the same time, which one will hit the ground first?
given\tunknown\tequation\tsubstitution\tanswer & units
δy =
vi =
a =
t =
if it takes the watermelon 1 second to reach the ground when it is thrown downward at 10 m/s, how tall are the stands?
unknown\tequation\tsubstitution\tanswer & units

Explanation:

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Problem 1a: Time to peak height

Step1: List given/unknown values

Given: $v_i = 58.8\ \text{m/s}$, $v_f = 0\ \text{m/s}$, $a = -9.8\ \text{m/s}^2$
Unknown: $t$

Step2: Select velocity-time equation

$v_f = v_i + at$

Step3: Solve equation for t

$t = \frac{v_f - v_i}{a}$

Step4: Substitute values

$t = \frac{0 - 58.8}{-9.8}$

Step5: Calculate final value

$t = 6\ \text{s}$

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Problem 1b: Peak height

Step1: List given/unknown values

Given: $v_i = 58.8\ \text{m/s}$, $v_f = 0\ \text{m/s}$, $a = -9.8\ \text{m/s}^2$, $t=6\ \text{s}$
Unknown: $\Delta y$

Step2: Select displacement equation

$\Delta y = v_i t + \frac{1}{2} a t^2$

Step3: Substitute values

$\Delta y = (58.8)(6) + \frac{1}{2}(-9.8)(6)^2$

Step4: Calculate final value

$\Delta y = 352.8 - 176.4 = 176.4\ \text{m}$

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Problem 2a: Fall time comparison

Step1: Recall free-fall principle

In vacuum/air resistance ignored, all objects accelerate at $a=-9.8\ \text{m/s}^2$ regardless of mass.

Step2: Conclude fall time result

Both objects hit the ground at the same time.

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Problem 2b: Height of stands

Step1: List given/unknown values

Given: $v_i = 10\ \text{m/s}$, $t=1\ \text{s}$, $a = 9.8\ \text{m/s}^2$
Unknown: $\Delta y$

Step2: Select displacement equation

$\Delta y = v_i t + \frac{1}{2} a t^2$

Step3: Substitute values

$\Delta y = (10)(1) + \frac{1}{2}(9.8)(1)^2$

Step4: Calculate final value

$\Delta y = 10 + 4.9 = 14.9\ \text{m}$

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Answer:

1a. 6 s
1b. 176.4 m
2a. The watermelon and pumpkin hit the ground at the same time.
2b. 14.9 m

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Filled Table Summaries:

1a Table:

Given	Unknown	Equation	Substitution	Answer & Units

1b Table:

Given	Unknown	Equation	Substitution	Answer & Units

2a Table:

Given	Unknown	Equation	Substitution	Answer & Units

2b Table:

Given	Unknown	Equation	Substitution	Answer & Units