Answer:
10 seconds
Step-by-step explanation:
AS it is given in the question that
h(t) = -5t² + 30t + 200 ...........................(i)
We have to find the time when it will touch the ground
so it will be touching the ground when its height from ground will be zero
i.e. h(t)=0
so equation (i) becomes
0 = -5t² + 30t + 200
Now we will solve this to get the value of t
Dividing whole equation with (-5) it will give us
t² - 6t - 40 = 0
Using the mid term breaking rule which will break the mid term and we will get the factors from the mid term
t² - 10t + 4t - 40 = 0
Now we will do the factorization of it
t(t-10)+4(t-10)=0
(t-10)(t+4)=0
so either
t-10 = 0 or t+4=0
t=10 or t= - 4
as t is time so it can not be negative
so
t=10 seconds will be the time in which it will touch the earth
Answer: 10 seconds
Step-by-step explanation:
When the object hits the ground, the height (y-value) is 0.
h(t) = -5t² + 30t + 200
0 = -5t² + 30t + 200 set height equal to zero
0 = -5(t² - 6t - 40) factored out -5
0 = -5(t - 10)(t + 4) factored the quadratic
0 = t - 10 0 = t + 4 applied the Zero Product Property
t = 10 t = -4 solved for t
↓
t = -4 is not valid (since time cannot be negative)
So, t = 10
