Answer:
The correct answer is 8 feet.
Step-by-step explanation:
Height of the dirt bike is given by the equation h = 16[tex]t^{2}[/tex] + 20 t +8.
Initial velocity of the dirt bike is 20 feet per second
Initial height of the dirt bike when it launches off the ramp is 8 feet.
To find the maximum h, we differentiate the function h with respect to t and equate the result to zero.
⇒ [tex]\frac{d}{dt}[/tex]h = 0 = 32t + 20
and second order differentiation of h gives [tex]\frac{d^{2}h}{dt^{2}}[/tex] = 32.
This gives the value of the function maximum at t = -0.625 seconds.
This is absurd as the value of t cannot be negative.
Thus the dirt bike is going to fall off the ramp and is not going to gain any height, making the height at t = 0 the maximum height attained by it.
