Suppose a ball is kicked horizontally off a mountain with an initial speed of 9.37 m/s. If the ball travels a horizontal distance of 85.0 m, how tall is the mountain?
Using the horizontal component of motion for which the velocity is constant, first determine the time of flight:
We can now use to obtain the height:
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To find the height of the mountain, you can use the equation:
[ d = \frac{1}{2} \times g \times t^2 ]
Where:
- ( d ) is the vertical distance (height of the mountain)
- ( g ) is the acceleration due to gravity (approximately ( 9.8 , \text{m/s}^2 ))
- ( t ) is the time taken for the ball to fall
The horizontal distance (( d )) is given as 85.0 m and the initial horizontal velocity (( v_0 )) is given as 9.37 m/s.
Using the formula ( d = v_0 \times t ), solve for ( t ).
Then, substitute ( t ) into the equation above to find the height of the mountain.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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