PLEASE PLEASE HELP ME!!

Question

The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 25.5 m/s is h = 2 + 25.5t − 4.9t² after t seconds.

a) Find the velocity (in m/s) after t seconds.

v(t) =?

b)Find the velocity (in m/s) after 2 seconds and after 4 seconds.

v(2) = ?

v(4) = ?

c)What is the value (in m/s) of v(t) when the projectile reaches its maximum height?

v(t)=?

When (in s) does the projectile reach its maximum height? (Round your answer to two decimal places.)

d)What is the maximum height (in m)? (Round your answer to two decimal places.)

e) When (in s) does it hit the ground? (Round your answer to two decimal places.)

f) With what velocity (in m/s) does it hit the ground? (Round your answer to two decimal places.)

Answer 1

h(t) = 2 +25.5t -4.9t^2

v(t) = 25.5 - 9.8t = velocity at time t

v(2) = 25.5 -9.8(2) = 25.5- 19.6 = 5.9 meters per second

v(4) = 25.5 -9.8(4) = 25.5 - 39.2 = -13.7 m/s, the negative sign meaning it's coming down

v(t) = 0 when it reaches max height

25.5 -9.8t = 0

t = 25.5/9.8 = about 2.6 seconds to reach max height

max height = about h(2.6) = 2 +25.5(2.6) - 4.9(2.6)^2

= 2+66.3 - 33.12

=68.3-33.1

=35.2 meters

it hits the ground when h(t)= 2 +25.5t -4.9t^2 = 0

4.9t^2 -25.5t -2= 0

use the quadratic formula

you should get a little more than twice the time to reach max height