The height of a projectile launched upward at a speed of 25 meters/second from a height of 70 meters is given by the function h(

Question

2 years ago

7

t)=-5sup(t,2)+25t+70. How long will it take the projectile to hit the ground?

1 answer:

N76 [4] · Answer 1 · 2023-11-14T16:27:45+03:00

6.5 s take the projectile to hit the ground.

<h3>What is projectile?</h3>

A projectile is any object thrown into space upon which the only acting force is gravity.

Given:

speed = 25 m/s

h(t) = -5t² + 25t + 70

height = 70 m

Time to reach maximum height

( u sin90)/2g

= 25/2*9.8

= 1.275s

Max height = u²Sin² $\theta$ /g

=25*25/9.8

=63.775

So, total height=63.775 + 70 = 133.775 m

Now, time to fall back to the ground

h = ut+(1/2)gt²

t² = (h- ut)2/g

u=0

H= 133.775 m

(133.775*2)/9.8= t²

t² = 27.3010

t= 5.225 s

Total time taken to hit ground

= 5.225 + 1.275

= 6.5 s

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