please answer both questions A Determine the distance from t

please answer both questions A.) Determine the distance from the ball to the ground 1 second after it was tosses

The following function takes t, number of seconds since a ball was tossed in the air, and gives H, the distance from the ball to the ground (in feet). 2. H(t) =-16t2 +90t + 5 Determine the distance from the ball to the ground 1 second after it was tossed. Determine how long it takes for the ball to hit the ground (in other words, determine when the distance drops to O feet)

Solution

A) In order to find distance from the ball to the ground 1 second after it was tosses we need to plugging t= 1 in the given equation of H(t). hence, we have

H(1) = -16 (1)^2 +90*1 +5

=> H(1) = -16+ 95

=> H(1) = 79

Hence required distance = 79 feet

B) When the ball hits the ground the distance H(t) = 0. Therefore, substitute H(t) = 0 and then find value of t

Hence, we have

-16t^2 +90t +5 =0

=> t= -90 +- sqrt(8420) / -32

=> t = 45 + - sqrt (2105) / 16

=> t= -0.055 , 5.68

T cannot be negative, hence we have

t= 5.68 seconds