The height, y meters, of a model rocket launced directly upwards from the ground can be modeled by y=96t-4t^2 where t is the time in seconds after it leaves the ground.
Answers
Given:
Height "y" metres of a rocket modeled by y = 96t - 4t² where t = time in seconds
To find:
a) Height of the rocket after 2 sec
b) Maximum height of the rocket
c) the time at which the rocket will hit the ground.
Solution:
Given height, y = 96t - 4t² --------------- (1)
a) The height of the rocket after 2 seconds can be calculated by substituting the value of t as 2 in the equation (1). So, by substituting we get,
⇒ y = 96 × 2 - 4*(2)^2
⇒ y = 192 - 16
⇒ y = 176 m
Hence, after 2 sec, the height will be 176 m.
b) Now, we will apply the formula t = -b/2a for finding the maximum height the rocket will attain. So, in the equation, a = -4, b = 96. Thus,
⇒ t = -b/2a
⇒ t = -96/2×(-4)
⇒ t = 12 seconds
Now, plug in 12 for t in the equation to get the maximum height:
⇒ y = 96 × 12 - 4*(12)^2
⇒ y = 576 m
Hence, the maximum height will be 576 m.
c) At y = 0, the rocket will hit the ground. So, setting y = 0,
⇒ y = 96t - 4t²
⇒ y = -4t( t-24 )
⇒ y = 24 sec.
Thus, after 14 sec the rocket will hit the ground.