View source for Proj Motion EX 12

''Helena Dedic''
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A ball is thrown from ground level. Three seconds later it is moving horizontally at 15 m/s. Find the horizontal range and the angle of impact. <br> <br>

'''Solution:''' <br><br>

At t = 2 s, the velocity of a projectile is v = (15 m/s, 0 m/s). What is the range of the flight and the angle of impact?
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[[image: Proj Motion Sol 12.png|TOP]] <br><br>

Since <math>v_y = 0</math>, the projectile must be at the top of its motion at t = 2 s. The total time of the motion is then 4 s and the range is given by equation 1:  <br>

 <math>\Delta x = v_{xo}t</math> <br>


 <math> \Delta x = 15 m/s * 4 s = 60 m</math> <br>


Find the velocity in the y-direction at impact taking the initial velocity as zero at the top and finding the velocity 2 s later: <br>


 <math>v_y = v_{yo} - 9.8 m/s^2 t</math> <br>


 <math>v_y = 0 - 9.8 m/s^2 2 s</math> <br>


 <math>v_y = - 19.6 m/s</math> <br>


The velocity at impact is v = (15 m/s, -19.6 m/s) so that the angle of impact is <math>52.6^o</math> below the horizontal or <math>-52.6^o</math>. <br>
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*[[Projectile Motion|Back to Projectile Motion]] <br><br>
*[[Exercises on Projectile Motion|Back to Exercises on Projectile Motion]] <br><br>