Ejemplo 2 Encontremos la velocidad de una bala de 0.02 kg que adquiere una energia cinética de 400 J. \( \begin{array}{lll}\text { Datos: } \\ m=0.02 \mathrm{~kg} & E_{k}=\frac{1}{2} m v^{2} \\ E_{k}=4001 & \frac{2 E_{k}}{m}=v^{2} & \begin{array}{l}\text { Despejamos la velocidad dejándola e } \\ \text { uno de los lados de la ecuación. }\end{array}\end{array} \)

\( \frac{\text { Exercice } 15}{\text { Deux charges électriques } q_{A}=1 \mathrm{mC} \text { et } \mathrm{q}_{\mathrm{B}}=-3 \mathrm{mC} \text { sont }} \) placées en A et B distants de 20 cm . 1) Détermine les caractéristiques du vecteur champ électrique au point M , milieu de AB (faire un schéma précis). 2) On remplace les deux charges \( \mathrm{q}_{\mathrm{A}} \) et \( \mathrm{q}_{\mathrm{B}} \) respectivement par \( \mathrm{q}_{1}=-2 \mu \mathrm{C} \) et \( \mathrm{q}_{2}=-5 \mu \mathrm{C} \). a) Détermine la valeur du champ électrique au point M . b) Quel doit être la position du point M pour avoir \( \mathrm{E}_{\mathrm{M}}=0 \) ?

Deux charges ponctuelles \( \mathrm{q}_{1}=10 \mu \mathrm{C} \) et \( \mathrm{q}_{2}=30 \mu \mathrm{C} \) sont placées respectivement en A et B distantes de 40 cm . 1) Calcule le module du champ électrique \( \overrightarrow{\mathrm{E}} \) au point M milieu de AB . 2) Détermine le point P de \( [\mathrm{AB}] \) où le champ est nul. 3) Détermine le module du champ électrique \( \overrightarrow{\mathrm{E}} \) a) En un point N situé entre A et B à 10 cm de A . Représente ce champ sur un schéma clair. b) En un point Q situé sur lá médiatrice de AB à 20 cm du milieu M de AB .

Ejemplo 2 Encontremos la velocidad de una bala de 0.02 kg que adquiere una energia cinética de 400 J. \( \begin{array}{lll}\text { Datos: } \\ m=0.02 \mathrm{~kg} & E_{k}=\frac{1}{2} m v^{2} \\ E_{k}=4001 & \frac{2 E_{k}}{m}=v^{2} & \begin{array}{l}\text { Despejamos la velocidad dejándola e } \\ \text { uno de los lados de la ecuación. }\end{array}\end{array} \)

प्रश्न 20. एक कण सरल आवर्त गति से एक सरल रेखा पर गतिमान है। जब कण की केन्द्र से दूरी \( x_{1} \) तथा \( x_{2} \) है तथा इसक वेग कमशः \( \nu_{1} \) तथा \( v_{2} \) है। सिद्ध कीजिये कि आवर्त काल होगा

11. A particle is projected into the air at a speed of \( 25 \mathrm{~m} / \mathrm{s} \) at an angle \( 40^{\circ} \) above the horizontal. (a) How long does it take the particle to reach its maximum height? (b) What is its horizontal distance covered? 12. A stone is projected with a speed of \( 17.32 \mathrm{~m} / \mathrm{s} \) at an angle of \( 60^{\circ} \) to the horizontal. Calculate the maximum height and the range covered by the stone. 13. A ball is projected horizontally from the edge of a platform at \( 12.0 \mathrm{~m} / \mathrm{s} \). If the platform is 8.0 m above the floor, what are the magnitude and direction of the ball's velocity as it hits the floor? 14. A particle is launched such that its maximum range is 26.4 m . What is the speed at which it is launched? 15. A rifle fires a bullet at \( 360 \mathrm{~m} / \mathrm{s} \). (a) At what angle must the rifle be positioned for the bullet to hit a target 242.4 m away at the same height as the rifle?(b) If gravitational force does not act on the bullet, how far above the target will the bullet pass maintaining the same angle? 16. A particle projected at an angle of \( \theta \) above the horizontal has a velocity of \( v=(16 i+5 j) \mathrm{m} / \mathrm{s} \) at time \( t=0.8 \mathrm{~s} \) after launching. (a) What is the maximum height of the particle? (b) What is the range of the particle? 17. A ball is kicked into the air. When it reaches the vertical height of 7.5 m , the velocity is measured to have a horizontal component of \( 10.4 \mathrm{~m} / \mathrm{s} \) and a vertical component of \( 3.7 \mathrm{~m} / \mathrm{s} \). Calculate the maximum height and horizontal distance, which the ball travels.