QuestionHow long does it take for a football to fall $1719 \mathrm{~m}$ on Mars? $(\mathrm{g}=3.72 \mathrm{~m}/\mathrm{s}^2)$ ?

Studdy Solution

STEP 1

Assumptions1. The height of the cliff is1719 m. The acceleration due to gravity on Mars is3.72 m/s^3. The football is dropped from rest (initial velocity is0)
4. We ignore air resistance

STEP 2

We will use the equation of motion that relates distance (height in this case), initial velocity, acceleration (gravity in this case), and time. The equation is $d = v_i t + \frac{1}{2} g t^2$ where- $d$ is the distance (or height in this case) - $v_i$ is the initial velocity- $t$ is the time- $g$ is the acceleration due to gravity

STEP 3

Since the football is dropped from rest, the initial velocity $v_i$ is0. This simplifies our equation to $d = \frac{1}{2} g t^2$

STEP 4

We want to solve for time $t$ , so we rearrange the equation to solve for $t$ $t = \sqrt{\frac{2d}{g}}$

STEP 5

Now, we can plug in the given values for the height of the cliff (d) and the acceleration due to gravity on Mars (g) to calculate the time.
$t = \sqrt{\frac{2 \times1719}{3.72}}$

STEP 6

Calculate the time it would take for the football to hit the ground.
$t = \sqrt{\frac{2 \times1719}{3.72}} \approx30.4 \, s$ So, it would take approximately30.4 seconds for the football to hit the ground.

Was this helpful?

QuestionHow long does it take for a football to fall $1719 \mathrm{~m}$ on Mars? $(\mathrm{g}=3.72 \mathrm{~m}/\mathrm{s}^2)$ ?

Studdy Solution

STEP 1

Assumptions1. The height of the cliff is1719 m. The acceleration due to gravity on Mars is3.72 m/s^3. The football is dropped from rest (initial velocity is0)
4. We ignore air resistance

STEP 2

STEP 3

Since the football is dropped from rest, the initial velocity $v_i$ is0. This simplifies our equation to $d = \frac{1}{2} g t^2$

STEP 4

We want to solve for time $t$ , so we rearrange the equation to solve for $t$ $t = \sqrt{\frac{2d}{g}}$

STEP 5

Now, we can plug in the given values for the height of the cliff (d) and the acceleration due to gravity on Mars (g) to calculate the time.
$t = \sqrt{\frac{2 \times1719}{3.72}}$

STEP 6

Calculate the time it would take for the football to hit the ground.
$t = \sqrt{\frac{2 \times1719}{3.72}} \approx30.4 \, s$ So, it would take approximately30.4 seconds for the football to hit the ground.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionHow long does it take for a football to fall 1719 m1719 \mathrm{~m}1719 m on Mars? (g=3.72 m/s2)(\mathrm{g}=3.72 \mathrm{~m}/\mathrm{s}^2)(g=3.72 m/s2)?

Studdy Solution

STEP 1

Assumptions1. The height of the cliff is1719 m. The acceleration due to gravity on Mars is3.72 m/s^3. The football is dropped from rest (initial velocity is0)4. We ignore air resistance

STEP 2

STEP 3

Since the football is dropped from rest, the initial velocity viv_ivi​ is0. This simplifies our equation tod=12gt2d = \frac{1}{2} g t^2d=21​gt2

STEP 4

We want to solve for time ttt, so we rearrange the equation to solve for tttt=2dgt = \sqrt{\frac{2d}{g}}t=g2d​​

STEP 5

Now, we can plug in the given values for the height of the cliff (d) and the acceleration due to gravity on Mars (g) to calculate the time.t=2×17193.72t = \sqrt{\frac{2 \times1719}{3.72}}t=3.722×1719​​

STEP 6

Calculate the time it would take for the football to hit the ground.t=2×17193.72≈30.4 st = \sqrt{\frac{2 \times1719}{3.72}} \approx30.4 \, st=3.722×1719​​≈30.4sSo, it would take approximately30.4 seconds for the football to hit the ground.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionHow long does it take for a football to fall $1719 \mathrm{~m}$ on Mars? $(\mathrm{g}=3.72 \mathrm{~m}/\mathrm{s}^2)$ ?

Assumptions1. The height of the cliff is1719 m. The acceleration due to gravity on Mars is3.72 m/s^3. The football is dropped from rest (initial velocity is0)
4. We ignore air resistance

Since the football is dropped from rest, the initial velocity $v_i$ is0. This simplifies our equation to $d = \frac{1}{2} g t^2$

We want to solve for time $t$ , so we rearrange the equation to solve for $t$ $t = \sqrt{\frac{2d}{g}}$

Now, we can plug in the given values for the height of the cliff (d) and the acceleration due to gravity on Mars (g) to calculate the time.
$t = \sqrt{\frac{2 \times1719}{3.72}}$

Calculate the time it would take for the football to hit the ground.
$t = \sqrt{\frac{2 \times1719}{3.72}} \approx30.4 \, s$ So, it would take approximately30.4 seconds for the football to hit the ground.