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 Aurora hit a baseball with an initial velocity of 70 feet per second at an angle of 30° with the horizontal. The ball hit her bat when the ball was 3 feet above the ground.

(a) No one interferes with the ball. How long does it take the ball to hit the ground? Round your answer to the nearest hundredth of a second. Show all your work.

(b) How far did the ball travel horizontally? Use your answer from Part (a) in your calculations. Round your answer to the nearest tenth of a foot. 

 Apr 19, 2020
 #1
avatar+9447 
+1

\(s=v_{horizontal}\times t\) Aurora hit a baseball with an initial velocity of 70 feet per second at an angle of 30° with the horizontal. The ball hit her bat when the ball was 3 feet above the ground.

(a) No one interferes with the ball. How long does it take the ball to hit the ground? Round your answer to the nearest hundredth of a second. Show all your work.

(b) How far did the ball travel horizontally? Use your answer from Part (a) in your calculations. Round your answer to the nearest tenth of a foot. 

 

Aurora schlug einen Baseball mit einer Anfangsgeschwindigkeit von 70 Fuß pro Sekunde in einem Winkel von 30 ° zur Horizontalen. Der Ball traf ihren Schläger, als der Ball 3 Fuß über dem Boden war.
(a) Niemand stört den Ball. Wie lange dauert es, bis der Ball auf dem Boden aufschlägt? Runden Sie Ihre Antwort auf die nächste Hundertstelsekunde. Zeigen Sie alle Ihre Arbeiten.
(b) Wie weit bewegte sich der Ball horizontal? Verwenden Sie Ihre Antwort aus Teil (a) in Ihren Berechnungen. Runden Sie Ihre Antwort auf den nächsten Zehntel Fuß.

It makes it easier for me.

 

Hallo lightsup!

 

(a)

\(\sum h=0\)

 

\(3ft+\frac{70ft}{sec}\cdot sin(30^0)\cdot t-\frac{g}{2}t^2=0\)

 

\(-\frac{32.185\cdot ft}{2\ sec^2}t^2+\frac{70ft}{sec}\cdot sin(30^0)\cdot t+3ft=0\\ -\frac{32.185}{2}t^2+70\cdot 0.5\cdot t+3=0\\ \color{blue}-16.0925\ t^2+35\ t+3=0\)

\(t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

\(t=\frac{-35\pm\sqrt{35^2+4*16.0925*3}}{-2*16.0925}\\ t=\frac{-35\pm 37.6578}{-32.185}\\ t=\frac{-72.6578}{-32.185}\)

\(t=2.26\ sec\)

 

(b)

\(s= v_{horizontal}*t\)

\(v_{horizontal}=70 \frac{ft}{sec}*cos(30^0)\)

\(s=70 \frac{ft}{sec}*cos(30^0)*2.257sec\)

\(s=136.9\ ft\)

laugh  !

 Apr 19, 2020
edited by asinus  Apr 19, 2020
edited by asinus  Apr 19, 2020
 #2
avatar+12182 
+2

(b) How far did the ball travel horizontally? Use your answer from Part (a) in your calculations. Round your answer to the nearest tenth of a foot. 

 

(a) No one interferes with the ball. How long does it take the ball to hit the ground? Round your answer to the nearest hundredth of a second. Show all your work.

 

laugh

 Apr 19, 2020
edited by Omi67  Apr 19, 2020
edited by Omi67  Apr 19, 2020

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