QuestionA cannonball is shot horizontally at from an cliff. Find its horizontal distance before impact.
Studdy Solution
STEP 1
Assumptions1. The initial velocity of the cannonball is50 m/s in the horizontal direction.
. The height from which the cannonball is launched is80 m.
3. The acceleration due to gravity is approximately9.8 m/s² downward.
4. Air resistance is negligible.
STEP 2
First, we need to find the time it takes for the cannonball to hit the ground. We can do this using the equation of motion for vertical displacement, which is given bywhere- is the height from which the cannonball is launched, - is the acceleration due to gravity, and- is the time it takes for the cannonball to hit the ground.
STEP 3
Now, plug in the given values for the height and acceleration due to gravity to calculate the time.
STEP 4
Calculate the time it takes for the cannonball to hit the ground.
STEP 5
Now that we have the time, we can find the horizontal distance the cannonball will travel before hitting the ground. This can be calculated using the formulawhere- is the horizontal distance, - is the initial horizontal velocity, and- is the time it takes for the cannonball to hit the ground.
STEP 6
Plug in the values for the initial horizontal velocity and the time to calculate the horizontal distance.
STEP 7
Calculate the horizontal distance the cannonball will travel before hitting the ground.
The cannonball will travel202 meters horizontally before hitting the ground.
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