Question

The distance of a ball thrown upward is given by h(t) = -2t^2 + 12t – 10 meters. Find the velocity of the ball when it returns to the ground.

Answer 1

x=2t^2+12t-10
dx/dt=4t+12
t=0 in above equation..
12ms^-1

Answer 2

differentiate

Answer 3

i dont know if my answer is correct...sorry if its wrong

Answer 4

hello

Answer 5

I think it is. I got that before and its definitely wrong sweetie :/

Answer 6

hey :) can anyone help me out? :/

Answer 7

-4t+12
=12ms^-1

Answer 8

@rhino..assuming that the ball is thrown at time t=0..we would get velocity of the ball when it hits the earth wouldnt we?shouldnt we consider the acceleration..??sorry if its nonsense

Answer 9

when on the ground t is 0
-4(0)+12
=12

Answer 10

are you sure it might not be 3,5,--8, or -10. I got 12 too but it seems to be wrong :( ughh

Answer 11

velocity cant be negative..becausse its a vector...

Answer 12

Thanks for trying everyone. :(

Answer 13

veloicty CAN be negative because it is vector

Answer 14

-4t+12=0
-4t=-12
t=3

-4(6)+12
-24+12=-12 m/s

Answer 15

hey....
magnitude of vector is always positive....

Answer 16

\[v(t)=-4t+12\]The ball comes to a rest at it's maximum height. Entering v=0:\[-4t=-12, t=3\]How high is the ball? We enter t=3 into position function:\[s(t)=-2(3)^2+12(3)-10=-18+36-10=8\]The ball will take the same amount of time to reach the ground as it did to reach the max height. The total time to go up and then back down is 6 sec. Inputting:\[v(6)=-4(6)+12=-12m/s\] This makes sense. The ball was released at an initial velocity of +12m/s (input t=0 into velocity function), comes to a stop under the action of gravity and reverses direction. When it reaches the same initial point it must have the same velocity as the initial velocity only in the opposite direction.

Answer 17

you are correct, magnitude is always positive but we are not trying to find magnitude

Answer 18

@imran ..The magnitude of a vector is always treated as non negative and the minus sign indicates the reversal of that vector through an angle of 180 degree.

http://wiki.answers.com/Q/Can_the_magnitude_of_a_vector_have_a_negative_value

Answer 19

magnitude of velocity is speed; the question ask for velocity;not speed

Answer 20

read my previous post

Answer 21

we are not finding magnitude, thus we don't need to worry about that

Answer 22

then what r we finding?

Answer 23

velocity which is a vector; not magnitude

Answer 24

magnitude is scalar

Answer 25

hey....vector has mag and dir... when u say he force is 20N due east ..u mean both dir and mag...even if u say the force is 20N it doesnt make force scalar..

Answer 26

exactly vector has both magnitude and direction, so in our case 12 is magnitude - is direction; which makes vector -12

Answer 27

moreover...u know representaion of vector?its represented using directed line segment and the length of the line segment gives magnitude...so length cant be negative...hence magnitude of vector cannot also be negative

Answer 28

I agree with you that magnitude can't be negative, which is absolutely correct. What I am saying is vector can be negative; not its magnitude

Answer 29

the answer is -8 :) thanks for trying everyone. -4(5) +12

Answer 30

Velocity can in fact be negative. Think outside the box d: if im going 30 miles an hour east but you're going 80 miles an hour west you're going to be going faster but in a different direction

Answer 31

Ah, I know why. The ball starts out at a position of x=-10m. If you define the "ground" to be x=0m than the answer is -8m/s as you say. I gave you the velocity when the ball returns to it's initial position of -10m NOT 0m.

Answer 32

oh yea the ball is coming down......

and hey why 5?

Answer 33

Hit the ground at t=5

Answer 34

Exactly :D

Answer 35

The question should read "find the velocity of the ball when it returns to h=0m"

Answer 36

I took the question as "find the velocity of the ball when it returns to it's initial position h=-10m"