Question

question 13 (mandatory) (1 point) saved
a rocket is launched into the sky and follows a path modelled by the function ( h(t) = -5(t - 6.32)^2 + 200 ), where time, ( t ), is in seconds and height, ( h(t) ), is in metres.
approximately how high will the rocket be after 9 seconds?

a) 200 m

b) 145 m

c) 187 m

d) 164 m

Explanation:

Step1: Substitute t = 9 into the function

We have the height function \( h(t) = -5(t - 6.32)^2 + 200 \). Substitute \( t = 9 \) into it: \( h(9) = -5(9 - 6.32)^2 + 200 \).

Step2: Calculate the value inside the parentheses

First, calculate \( 9 - 6.32 = 2.68 \).

Step3: Square the result

Then, square \( 2.68 \): \( 2.68^2 = 7.1824 \).

Step4: Multiply by -5

Multiply this result by -5: \( -5\times7.1824 = -35.912 \).

Step5: Add 200

Finally, add 200 to the result: \( h(9) = -35.912 + 200 = 164.088 \approx 164 \) (rounded to the nearest whole number).

Answer:

d) 164 m