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?

Answer 1

#403.1"m"#

Using the horizontal component of motion for which the velocity is constant, first determine the time of flight:

#t=s/v=85/9.37=9.07"s"#

We can now use to obtain the height:

#h=1/2"g"t^2#
#:.h=0.5xx9.8xx9.07^2=403.1"m"#
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Answer 2

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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Answer from HIX Tutor

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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