*80.  A baseball player hits a home run, and the ball lands in the left-field seats, 7.5 m above the point at which it was hit. It lands with a velocity of 36 m/s at an angle of 28° below the horizontal (see the drawing). The positive directions are upward and to the right in the drawing. Ignoring air resistance, find the magnitude and direction of the initial velocity with which the ball leaves the bat.

 

Since there is no air resistance, we know the x component of velocity does not change.

 

 

For the vertical motion we know the change in height, since we do not have a time we use the following relationship

Therefore

Now use the Pythagorean theorem

 

 

 

 

Now plug in values

 

 

We can find the angle by using tangent function

 

 

 

 

 

 

 

Alternatively find angle by

 

 

As we found before!

 

 

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This page last updated on January 11, 2020