The equation for projectile motion in feet is $h(t)=-16t^2+v_0t+h_0$ where $v_0$ is the initial velocity in ft/s and $h_0$ is the initial height in feet.

We are given that the initial upward velocity is $v_0=150ft/sec$ and the initial height is $h_0=35ft$ . Thus, plugging these values into our equation, we get $h(t)=-16t^2+150t+35$ as our equation for the situation.

The firework will land, assuming it doesn't explode, when $h(t)=0$ , thus:

$h(t)=-16t^2+150t+35\\\\0=-16t^2+150t+35\\\\t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\t=\frac{-150\pm\sqrt{150^2-4(-16)(35)}}{2(-16)}\\ \\t=\frac{-150\pm\sqrt{22500+2240}}{-32}\\\\t=\frac{-150\pm\sqrt{24740}}{-32}\\\\t=\frac{-150\pm2\sqrt{6185}}{-32}\\ \\t=\frac{75\pm\sqrt{6185}}{16}\\\\t_1\approx-0.2\\\\t_2\approx9.6$

Since time can't be negative, then the firework will land after 9.6 seconds, assuming it doesn't explode at the time of landing.

3 0

3 years ago

Question down below down below

ser-zykov [4K]

Answer:

Step-by-step explanation:

y = 2.5 x - 57

y = Profit: 143

143 = 2.5 x - 57 Add 57 to both sides

143 + 57 = 2x - 57 + 57 Combine like terms

200 = 2.5 x Divide by 2.5

200/2.5 = 2.5x/2.5

x = 80 plants

3 0

3 years ago

Help me please thank you

Elan Coil [88]

Answer:

23/3

Step-by-step explanation:

They already give you the area of one base, which is great! The volume of a rectangular prism is l · w · h, and they've already done h · l for you.

All you do is multiply the two values you see on screen.

4/3 · 23/ 4

= 23/3

(Since there is a 4 both on top and on the bottom, you can cross them out, instead of multiplying everything across)

I hope this helped!

3 0

3 years ago