a 30lb- force below the origin, a 20lb-force 3ft above the origin and making an angle of30° N of E, a 100lb-force with a horizontal distance of 3ft and a vertical distance of4ft from the origin and making an angle of 45° NW, a 60lb-force with the samedistance like the previous force but along the positive x-axis, and a 100lb- force 4ft tothe right of the origin and making an angle of 60° S of W. Determine the magnitude andEasily sign with your fingers in PDFSign5. Derive a formula that relates the displacement, final velocity, time and constantacceleration of an object in UARM (Uniformly Accelerated Rectilinear Motion). Use thatformula to find the time it takes for a particle to attain a velocity of 30"", given that theconstant acceleration is 6 and the particle's displacement is 25m to the left of theorigin.6. Suppose an electron has an acceleration defined by a, (t) = 30te-t, wheret is inseconds. Find the position as a function of time and determine how far the electron wouldbe fromthe origin when it momentarily stops.7. Simple Harmonic Motion is defined as a periodic motion of a point along a straight line,such that its acceleration is always towards a fixed point in that line and is proportional toits distance from that point. In other words, its acceleration is proportional to thedisplacement but acts in an opposite direction. Prove algebraically that the motion of aparticle defined by x = cos 2t + 2sin2t is simple harmonic.8. You fire a ball with an initial speed of v at an angle o above the surface of an incline,which is itself inclined at anangle 0 above the horizontal.a) Find the distance, measured along the indline, from the launch point to the pointwhen the ball strikes the incline.b) What angle o gives the maximum range, measured along the incline? Ignore airresistance.9. According to the Guinness Book of World Records, the longest home run ever measuredwas hit by Roy “Dizzy" Carlyle in a minor league game. The ball travelled 188m beforelanding on the ground outside the ballpark. Assuming the ball's initial velocity was in adirection 45° above the horizontal, what did the initial speed of the ball need to be toproduce such a home run if the ball was hit at a point 0.9m above ground level? Ignoreair resistance.10. A small toy airplane is flying in the xy – plane parallel to the ground. During the timeintervaltį = 0s andt21s, its velocity as a function of time is given by3 = 1.2ti + (12" - 2)mmmAt what values of t is the velocity of the plane perpendicular to its acceleration?End

Name: a 30lb- force below the origin, a 20lb-force 3ft above the origin and
Uploaded: 2024-03-05T11:56:34.000Z
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Description: a 30lb- force below the origin, a 20lb-force 3ft above the origin and making an angle of30° N of E, a 100lb-force with a horizontal distance of 3ft and a vertical distance of4ft from the origin and making an angle of 45° NW, a 60lb-force with the sa

Question

a 30lb- force below the origin, a 20lb-force 3ft above the origin and making an angle of30° N of E, a 100lb-force with a horizontal distance of 3ft and a vertical distance of4ft from the origin and making an angle of 45° NW, a 60lb-force with the samedistance like the previous force but along the positive x-axis, and a 100lb- force 4ft tothe right of the origin and making an angle of 60° S of W. Determine the magnitude andEasily sign with your fingers in PDFSign5. Derive a formula that relates the displacement, final velocity, time and constantacceleration of an object in UARM (Uniformly Accelerated Rectilinear Motion). Use thatformula to find the time it takes for a particle to attain a velocity of 30&#34;&#34;, given that theconstant acceleration is 6 and the particle's displacement is 25m to the left of theorigin.6. Suppose an electron has an acceleration defined by a, (t) = 30te-t, wheret is inseconds. Find the position as a function of time and determine how far the electron wouldbe fromthe origin when it momentarily stops.7. Simple Harmonic Motion is defined as a periodic motion of a point along a straight line,such that its acceleration is always towards a fixed point in that line and is proportional toits distance from that point. In other words, its acceleration is proportional to thedisplacement but acts in an opposite direction. Prove algebraically that the motion of aparticle defined by x = cos 2t + 2sin2t is simple harmonic.8. You fire a ball with an initial speed of v at an angle o above the surface of an incline,which is itself inclined at anangle 0 above the horizontal.a) Find the distance, measured along the indline, from the launch point to the pointwhen the ball strikes the incline.b) What angle o gives the maximum range, measured along the incline? Ignore airresistance.9. According to the Guinness Book of World Records, the longest home run ever measuredwas hit by Roy “Dizzy&#34; Carlyle in a minor league game. The ball travelled 188m beforelanding on the ground outside the ballpark. Assuming the ball's initial velocity was in adirection 45° above the horizontal, what did the initial speed of the ball need to be toproduce such a home run if the ball was hit at a point 0.9m above ground level? Ignoreair resistance.10. A small toy airplane is flying in the xy – plane parallel to the ground. During the timeintervaltį = 0s andt21s, its velocity as a function of time is given by3 = 1.2ti + (12&#34; - 2)mmmAt what values of t is the velocity of the plane perpendicular to its acceleration?End

Accepted Answer

Let u be the initial distance, v be the final velocity, a be the acceleration and S be the distance.…