Hi all,
I was just trying to run through a question sheet issued by my school on the Motion topic and got stuck / confused by a couple of the questions.
1) If a certain object has velocity v = 8x<SUP>2</SUP>, and if x = 2 when t = 1, then find:
(i) a in terms of x.
---Im not even sure what a</I> even stands for. As far as I know there can only be an amplitude if its in SHM, and this doesnt appear to be. a could possibly mean acceleration, though I seriously doubt it---
EDIT: Solved. Acceleration = v . dv / dx
2) An object falling directly to earth from space moves according to the equation d<SUP>2</SUP>x / dt<SUP>2</SUP> = -k / x<SUP>2<SUP>
where x is the distance of the object from the centre of the earth at time t. The constant k is related to g, the value of gravity at the eath's surface, and the radius of the earth, R, by the formula k = gR<SUP>2</SUP>. Show that if the particle started from rest at a distance of 10<SUP>9</SUP> from the earth's centre, then it would reach the earth with a velocity of approximately 11200m/s. (Assume R = 6.4 x 10<SUP>6</SUP>m and g = 9.8 m/s<SUP>2</SUP>)
---I got something around 15000m/s. Also I wasnt sure whether to take the centre of the earth as the 'earth', or to halve the radius and take the surface of the earth as the 'earth'. Either way I was still wrong :/----
EDIT: Solved. Was halving the radius. GG maths retardation
3) A six is scored in a cricket game when the blal is hit over the boundary fence on the full. A ball is hit from O with velocity V = 32m/s at an angle Z to the horizontal and towards the 1 metre high boundary fence 100 metres away.
(a) Show that the ball just clears the boundary when
50000tan<SUP>2</SUP>Z - 102400tanZ +51024 = 0
---I got something which vaguely resembled this but was still a fair ways off. The numbers were generally the same but I was a few trig's short---
Any help would really be appreciated !
</SUP></SUP>
EDIT: Solved thanks to you guys
I was just trying to run through a question sheet issued by my school on the Motion topic and got stuck / confused by a couple of the questions.
1) If a certain object has velocity v = 8x<SUP>2</SUP>, and if x = 2 when t = 1, then find:
(i) a in terms of x.
---Im not even sure what a</I> even stands for. As far as I know there can only be an amplitude if its in SHM, and this doesnt appear to be. a could possibly mean acceleration, though I seriously doubt it---
EDIT: Solved. Acceleration = v . dv / dx
2) An object falling directly to earth from space moves according to the equation d<SUP>2</SUP>x / dt<SUP>2</SUP> = -k / x<SUP>2<SUP>
where x is the distance of the object from the centre of the earth at time t. The constant k is related to g, the value of gravity at the eath's surface, and the radius of the earth, R, by the formula k = gR<SUP>2</SUP>. Show that if the particle started from rest at a distance of 10<SUP>9</SUP> from the earth's centre, then it would reach the earth with a velocity of approximately 11200m/s. (Assume R = 6.4 x 10<SUP>6</SUP>m and g = 9.8 m/s<SUP>2</SUP>)
---I got something around 15000m/s. Also I wasnt sure whether to take the centre of the earth as the 'earth', or to halve the radius and take the surface of the earth as the 'earth'. Either way I was still wrong :/----
EDIT: Solved. Was halving the radius. GG maths retardation
3) A six is scored in a cricket game when the blal is hit over the boundary fence on the full. A ball is hit from O with velocity V = 32m/s at an angle Z to the horizontal and towards the 1 metre high boundary fence 100 metres away.
(a) Show that the ball just clears the boundary when
50000tan<SUP>2</SUP>Z - 102400tanZ +51024 = 0
---I got something which vaguely resembled this but was still a fair ways off. The numbers were generally the same but I was a few trig's short---
Any help would really be appreciated !
</SUP></SUP>
EDIT: Solved thanks to you guys
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