QuestionA cannonball is fired horizontally from an 80 m cliff at 80 m/s. How far does it travel horizontally before hitting the ground?

Studdy Solution

STEP 1

Assumptions1. The height of the cliff is80.0 m. The initial horizontal velocity of the cannonball is80.0 m/s3. The initial vertical velocity of the cannonball is0 m/s (since it is fired horizontally)
4. The acceleration due to gravity is -9.8 m/s² (negative because it acts downwards)
5. The cannonball is not subject to any air resistance or any other forces except gravity

STEP 2

We first need to find the time it takes for the cannonball to hit the ground. We can use the equation of motion for this $t = \sqrt{\frac{2h}{g}}$ where- $t$ is the time, - $h$ is the height of the cliff, and- $g$ is the acceleration due to gravity.

STEP 3

Now, plug in the given values for the height of the cliff and the acceleration due to gravity to calculate the time.
$t = \sqrt{\frac{2 \times80.0\,m}{9.8\,m/s^2}}$

STEP 4

Calculate the time it takes for the cannonball to hit the ground.
$t = \sqrt{\frac{2 \times80.0\,m}{9.8\,m/s^2}} \approx4.04\,s$

STEP 5

Now that we have the time, we can find the horizontal distance the cannonball will fly before it hits the ground. We can use the formula $d = v \times t$ where- $d$ is the distance, - $v$ is the horizontal velocity, and- $t$ is the time.

STEP 6

Plug in the values for the horizontal velocity and the time to calculate the distance.
$d =80.0\,m/s \times4.04\,s$

STEP 7

Calculate the horizontal distance the cannonball will fly before it hits the ground.
$d =80.0\,m/s \times4.04\,s \approx323.2\,m$ The cannonball will fly approximately323.2 meters horizontally before it strikes the ground.

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QuestionA cannonball is fired horizontally from an 80 m cliff at 80 m/s. How far does it travel horizontally before hitting the ground?

Studdy Solution

STEP 1

STEP 2

We first need to find the time it takes for the cannonball to hit the ground. We can use the equation of motion for this $t = \sqrt{\frac{2h}{g}}$ where- $t$ is the time, - $h$ is the height of the cliff, and- $g$ is the acceleration due to gravity.

STEP 3

Now, plug in the given values for the height of the cliff and the acceleration due to gravity to calculate the time.
$t = \sqrt{\frac{2 \times80.0\,m}{9.8\,m/s^2}}$

STEP 4

Calculate the time it takes for the cannonball to hit the ground.
$t = \sqrt{\frac{2 \times80.0\,m}{9.8\,m/s^2}} \approx4.04\,s$

STEP 5

Now that we have the time, we can find the horizontal distance the cannonball will fly before it hits the ground. We can use the formula $d = v \times t$ where- $d$ is the distance, - $v$ is the horizontal velocity, and- $t$ is the time.

STEP 6

Plug in the values for the horizontal velocity and the time to calculate the distance.
$d =80.0\,m/s \times4.04\,s$

STEP 7

Calculate the horizontal distance the cannonball will fly before it hits the ground.
$d =80.0\,m/s \times4.04\,s \approx323.2\,m$ The cannonball will fly approximately323.2 meters horizontally before it strikes the ground.

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QuestionA cannonball is fired horizontally from an 80 m cliff at 80 m/s. How far does it travel horizontally before hitting the ground?

Studdy Solution

STEP 1

STEP 2

We first need to find the time it takes for the cannonball to hit the ground. We can use the equation of motion for thist=2hgt = \sqrt{\frac{2h}{g}}t=g2h​​where- ttt is the time, - hhh is the height of the cliff, and- ggg is the acceleration due to gravity.

STEP 3

Now, plug in the given values for the height of the cliff and the acceleration due to gravity to calculate the time.t=2×80.0 m9.8 m/s2t = \sqrt{\frac{2 \times80.0\,m}{9.8\,m/s^2}}t=9.8m/s22×80.0m​​

STEP 4

Calculate the time it takes for the cannonball to hit the ground.t=2×80.0 m9.8 m/s2≈4.04 st = \sqrt{\frac{2 \times80.0\,m}{9.8\,m/s^2}} \approx4.04\,st=9.8m/s22×80.0m​​≈4.04s

STEP 5

Now that we have the time, we can find the horizontal distance the cannonball will fly before it hits the ground. We can use the formulad=v×td = v \times td=v×twhere- ddd is the distance, - vvv is the horizontal velocity, and- ttt is the time.

STEP 6

Plug in the values for the horizontal velocity and the time to calculate the distance.d=80.0 m/s×4.04 sd =80.0\,m/s \times4.04\,sd=80.0m/s×4.04s

STEP 7

Calculate the horizontal distance the cannonball will fly before it hits the ground.d=80.0 m/s×4.04 s≈323.2 md =80.0\,m/s \times4.04\,s \approx323.2\,md=80.0m/s×4.04s≈323.2mThe cannonball will fly approximately323.2 meters horizontally before it strikes the ground.

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We first need to find the time it takes for the cannonball to hit the ground. We can use the equation of motion for this $t = \sqrt{\frac{2h}{g}}$ where- $t$ is the time, - $h$ is the height of the cliff, and- $g$ is the acceleration due to gravity.

Now, plug in the given values for the height of the cliff and the acceleration due to gravity to calculate the time.
$t = \sqrt{\frac{2 \times80.0\,m}{9.8\,m/s^2}}$

Calculate the time it takes for the cannonball to hit the ground.
$t = \sqrt{\frac{2 \times80.0\,m}{9.8\,m/s^2}} \approx4.04\,s$

Now that we have the time, we can find the horizontal distance the cannonball will fly before it hits the ground. We can use the formula $d = v \times t$ where- $d$ is the distance, - $v$ is the horizontal velocity, and- $t$ is the time.

Plug in the values for the horizontal velocity and the time to calculate the distance.
$d =80.0\,m/s \times4.04\,s$

Calculate the horizontal distance the cannonball will fly before it hits the ground.
$d =80.0\,m/s \times4.04\,s \approx323.2\,m$ The cannonball will fly approximately323.2 meters horizontally before it strikes the ground.