you shoot an arrow into the air. two seconds later the arrow has gone straight upward to a height of 40m and c?

d = ½at² + v₀t + d₀

d is displacenemt

v₀ is initial velocity

d₀ is initial position

d₀ = 0

40 = –½(9.8)(2)² + v₀2

2v₀ = 40 + 19.6

v₀ = 29.8 m/s (a)

h = v²/2g = 29.8²/2•9.8 = 45.3 m (b)

Time to reach peak is t = √(2h/g)

t = 3.04 s

so after 4 seconds it is on the way back down, by 0.96 sec

v = gt = 9.8•0.96 = 9.41 m/s (c)

H = Vo t + 1/2 g t^2 At t=2 , H= 40

40 = Vo (2) + 4,9 (2)^2

Vo = 29.4 m/s This is the Initial velocity

Final velocity at peak height Vf = 0 = Vo - g t

= 29.4 - 9.8 t

t = 3 s Time to peak height

Peak height = H = Vo t - 1/2 g t^2

= 29.4 (3) - 4.9 (3)^2 = 44.1 m

Velocity at t= 4 is V = Vo - g t

= 29.4 - 9.8(4) = - 9.8 down

Or you can start from peak height where Vo = 0 and the velocity at t=1 becomes Vo + gt = 0 + 9.8 (1) = 9.8m/s

When H = 30 , t=?

H = Vo t - 1/2 g t^2

30 = 29.4 t - 4.9 t^2

t^2 - 6 t + 6.12 = 0

Use the quadratic equation to get t= 1.3 s and t = 4.7 s

a) In two seconds it has gone 40 m.

In two seconds it has lost (2 x 9.8 m/s) 19.6 m/s in velocity from the effect of gravity.

For those two seconds the average speed was 20 m/s - because it traveled 40 m.

[Vo + (Vo - 19.6)]/2 = 20

Vo + Vo - 19.6 = 40

2Vo = 59.6

Vo = 29.8 m/s = Initial Velocity.

b) If we divide 29.8 by 9.8 we find that the arrow will rise for 3.04 seconds.

Its average speed during that time will be (29.8 + 0)/2 = 14.9 m/sec.

14.9 m/s x 3.04 seconds = 45.3 m

c) At t = 4 seconds the arrow will have been falling back to earth for .96 seconds.

Speed will be .96m/s x 9.8 m/s/s = 9.4 m/s

(Sorry,... I've gotta run...

Best,

Richard

The equation for top of the arrow is v0 t-0.5at^2 the place v0 is the preliminary speed, a is 9.8 m/s^2 and t is the time of flight. in case you put in 2 s for the time, set the top to 32 m and resolve for v0 you get 25.8 m/s which you obtain. Now, in case you place the top as sixteen m, v0 as 25.8 m/s, you get a quadratic equation in t: 25.8 t - 4.9 t^2 = sixteen. fixing for t provides 2 solutions, the main lifelike being 0.seventy two s.