Question

A stone is thrown upward from ground level. With what minimum speed should the stone be thrown so as to reach a height of 100 feet?

Answer 1

2) A falling stone is at a certain instant 204 feet above the ground. 2 seconds later it is only 12 feet above the ground. From what height was it dropped?

Answer 2

which one are we doing? i think you are supposed to use
\[h(t)=-16t^2+v_0t+h_0\]

Answer 3

first one

Answer 4

if we are doing the first one, since you are starting at "ground level"
\[h_0=0\] so you need to solve
\[-16t^2+v_0t\geq 100\] for v0

Answer 5

using the kinematic formula for motion in 2 dimension:
\[v_f^2 = v_i^2 + 2a(y_f-yi)\]
Where the height it must reach is 100 feet, and you know g=9.8 m/s^2, the right hand side of equation becomes:
\[v_f^2 = v_i^2 + 2(-9.8)(100)\]
\[(v_f^2 - v_i^2)= 2(-9.8)(100)\]
As the stone reaches max hieght, the velocity is zero
\[((0)^2 - v_i^2)= 2(-9.8)(100)\]
\[v_f= \sqrt{2(9.8)(100)}\]
\[v_i=14\sqrt{10} ft/s\]

Answer 6

we are doing both aslo

Answer 7

in other words make sure the equation
\[-16t^2+v_0t-100=0\] has a solution. use the quadratic formula and make sure the discriminant is positive

Answer 8

the answer choices for teh first one are 80, 112, 88, 96 or 78

Answer 9

you wold get
\[t=\frac{-v_0\pm\sqrt{v_0^2+6400}}{-32}\] so you have to make sure that
\[v_0^2+6400\geq 0\]

Answer 10

and therefore
\[v_0\geq80\]

Answer 11

so 80 wud b the answer rite

Answer 12

what about number 2

Answer 13

i made a mistake it should be
\[v_0^2-6400\geq 0\]

Answer 14

ok in the second one the stone was dropped, so you know
\[v_0=0\] but you do not know
\[h_0\]

Answer 15

so the equation will look like
\[h(t)=-16t^2+h_0\]

Answer 16

you know that for a certain t,
\[h(t)=-16t^2+h_0=240\] and that for t + 2 it is
\[h(t+2)=-16(t+2)^2+h_0=12\] you have to expand the second one and then you will have two equations involving h0 and t, you can solve for both

Answer 17

the answer chocies for teh second q are 271, 270, 266, 268, or 269

Answer 18

im confused...i expanded it adn got
-16t^2 +66h +ht +64 +h0....but we dont evn have teh time